How to find combinations with a matrix - ACT Math
Card 0 of 27
Matthew, Emily, Cynthia, John, and Stephanie are all running for student council. If three equivalent positions are available in this year's election, how many different leadership boards are possible?
Matthew, Emily, Cynthia, John, and Stephanie are all running for student council. If three equivalent positions are available in this year's election, how many different leadership boards are possible?
One possible approach is to enumerate all possibilities using initials for names (ie. MEC, MEJ, MES, etc). If we recognize that order does not matter in this problem, we can also enter 
into our calculators, and that will give us the answer of 
.
One possible approach is to enumerate all possibilities using initials for names (ie. MEC, MEJ, MES, etc). If we recognize that order does not matter in this problem, we can also enter
Compare your answer with the correct one above
Simplify.
Simplify.
When we are asked to simplify a matrix that is being multiplied by a constant we simply multiply each component of the matrix with the scalar factor that is on the outside of the matrix.
Therefore,
When we are asked to simplify a matrix that is being multiplied by a constant we simply multiply each component of the matrix with the scalar factor that is on the outside of the matrix.
Therefore,
Compare your answer with the correct one above
At a sale, a necklace that was originally 
is marked ten percent off. Cara has a coupon that will allow her to get ten percent off the discounted price. How much will Cara pay for the necklace if she uses the coupon?
At a sale, a necklace that was originally
Taking ten percent off of 
gives us 
,
.
Taking ten percent off of this amount gives us 
.
NOTE: This problem cannot be solved by taking twenty percent off of 
.
Taking ten percent off of
Taking ten percent off of this amount gives us
NOTE: This problem cannot be solved by taking twenty percent off of
Compare your answer with the correct one above
Matthew, Emily, Cynthia, John, and Stephanie are all running for student council. If three equivalent positions are available in this year's election, how many different leadership boards are possible?
Matthew, Emily, Cynthia, John, and Stephanie are all running for student council. If three equivalent positions are available in this year's election, how many different leadership boards are possible?
One possible approach is to enumerate all possibilities using initials for names (ie. MEC, MEJ, MES, etc). If we recognize that order does not matter in this problem, we can also enter into our calculators, and that will give us the answer of .
One possible approach is to enumerate all possibilities using initials for names (ie. MEC, MEJ, MES, etc). If we recognize that order does not matter in this problem, we can also enter
Compare your answer with the correct one above
Simplify.
Simplify.
When we are asked to simplify a matrix that is being multiplied by a constant we simply multiply each component of the matrix with the scalar factor that is on the outside of the matrix.
Therefore,
When we are asked to simplify a matrix that is being multiplied by a constant we simply multiply each component of the matrix with the scalar factor that is on the outside of the matrix.
Therefore,
Compare your answer with the correct one above
At a sale, a necklace that was originally is marked ten percent off. Cara has a coupon that will allow her to get ten percent off the discounted price. How much will Cara pay for the necklace if she uses the coupon?
At a sale, a necklace that was originally
Taking ten percent off of gives us ,
.
Taking ten percent off of this amount gives us
.
NOTE: This problem cannot be solved by taking twenty percent off of .
Taking ten percent off of
Taking ten percent off of this amount gives us
NOTE: This problem cannot be solved by taking twenty percent off of
Compare your answer with the correct one above
Matthew, Emily, Cynthia, John, and Stephanie are all running for student council. If three equivalent positions are available in this year's election, how many different leadership boards are possible?
Matthew, Emily, Cynthia, John, and Stephanie are all running for student council. If three equivalent positions are available in this year's election, how many different leadership boards are possible?
One possible approach is to enumerate all possibilities using initials for names (ie. MEC, MEJ, MES, etc). If we recognize that order does not matter in this problem, we can also enter into our calculators, and that will give us the answer of .
One possible approach is to enumerate all possibilities using initials for names (ie. MEC, MEJ, MES, etc). If we recognize that order does not matter in this problem, we can also enter
Compare your answer with the correct one above
Simplify.
Simplify.
When we are asked to simplify a matrix that is being multiplied by a constant we simply multiply each component of the matrix with the scalar factor that is on the outside of the matrix.
Therefore,
When we are asked to simplify a matrix that is being multiplied by a constant we simply multiply each component of the matrix with the scalar factor that is on the outside of the matrix.
Therefore,
Compare your answer with the correct one above
At a sale, a necklace that was originally is marked ten percent off. Cara has a coupon that will allow her to get ten percent off the discounted price. How much will Cara pay for the necklace if she uses the coupon?
At a sale, a necklace that was originally
Taking ten percent off of gives us ,
.
Taking ten percent off of this amount gives us
.
NOTE: This problem cannot be solved by taking twenty percent off of .
Taking ten percent off of
Taking ten percent off of this amount gives us
NOTE: This problem cannot be solved by taking twenty percent off of
Compare your answer with the correct one above
Matthew, Emily, Cynthia, John, and Stephanie are all running for student council. If three equivalent positions are available in this year's election, how many different leadership boards are possible?
Matthew, Emily, Cynthia, John, and Stephanie are all running for student council. If three equivalent positions are available in this year's election, how many different leadership boards are possible?
One possible approach is to enumerate all possibilities using initials for names (ie. MEC, MEJ, MES, etc). If we recognize that order does not matter in this problem, we can also enter into our calculators, and that will give us the answer of .
One possible approach is to enumerate all possibilities using initials for names (ie. MEC, MEJ, MES, etc). If we recognize that order does not matter in this problem, we can also enter
Compare your answer with the correct one above
Simplify.
Simplify.
When we are asked to simplify a matrix that is being multiplied by a constant we simply multiply each component of the matrix with the scalar factor that is on the outside of the matrix.
Therefore,
When we are asked to simplify a matrix that is being multiplied by a constant we simply multiply each component of the matrix with the scalar factor that is on the outside of the matrix.
Therefore,
Compare your answer with the correct one above
At a sale, a necklace that was originally is marked ten percent off. Cara has a coupon that will allow her to get ten percent off the discounted price. How much will Cara pay for the necklace if she uses the coupon?
At a sale, a necklace that was originally
Taking ten percent off of gives us ,
.
Taking ten percent off of this amount gives us
.
NOTE: This problem cannot be solved by taking twenty percent off of .
Taking ten percent off of
Taking ten percent off of this amount gives us
NOTE: This problem cannot be solved by taking twenty percent off of
Compare your answer with the correct one above
Matthew, Emily, Cynthia, John, and Stephanie are all running for student council. If three equivalent positions are available in this year's election, how many different leadership boards are possible?
Matthew, Emily, Cynthia, John, and Stephanie are all running for student council. If three equivalent positions are available in this year's election, how many different leadership boards are possible?
One possible approach is to enumerate all possibilities using initials for names (ie. MEC, MEJ, MES, etc). If we recognize that order does not matter in this problem, we can also enter into our calculators, and that will give us the answer of .
One possible approach is to enumerate all possibilities using initials for names (ie. MEC, MEJ, MES, etc). If we recognize that order does not matter in this problem, we can also enter
Compare your answer with the correct one above
Simplify.
Simplify.
When we are asked to simplify a matrix that is being multiplied by a constant we simply multiply each component of the matrix with the scalar factor that is on the outside of the matrix.
Therefore,
When we are asked to simplify a matrix that is being multiplied by a constant we simply multiply each component of the matrix with the scalar factor that is on the outside of the matrix.
Therefore,
Compare your answer with the correct one above
At a sale, a necklace that was originally is marked ten percent off. Cara has a coupon that will allow her to get ten percent off the discounted price. How much will Cara pay for the necklace if she uses the coupon?
At a sale, a necklace that was originally
Taking ten percent off of gives us ,
.
Taking ten percent off of this amount gives us
.
NOTE: This problem cannot be solved by taking twenty percent off of .
Taking ten percent off of
Taking ten percent off of this amount gives us
NOTE: This problem cannot be solved by taking twenty percent off of
Compare your answer with the correct one above
Matthew, Emily, Cynthia, John, and Stephanie are all running for student council. If three equivalent positions are available in this year's election, how many different leadership boards are possible?
Matthew, Emily, Cynthia, John, and Stephanie are all running for student council. If three equivalent positions are available in this year's election, how many different leadership boards are possible?
One possible approach is to enumerate all possibilities using initials for names (ie. MEC, MEJ, MES, etc). If we recognize that order does not matter in this problem, we can also enter into our calculators, and that will give us the answer of .
One possible approach is to enumerate all possibilities using initials for names (ie. MEC, MEJ, MES, etc). If we recognize that order does not matter in this problem, we can also enter
Compare your answer with the correct one above
Simplify.
Simplify.
When we are asked to simplify a matrix that is being multiplied by a constant we simply multiply each component of the matrix with the scalar factor that is on the outside of the matrix.
Therefore,
When we are asked to simplify a matrix that is being multiplied by a constant we simply multiply each component of the matrix with the scalar factor that is on the outside of the matrix.
Therefore,
Compare your answer with the correct one above
At a sale, a necklace that was originally is marked ten percent off. Cara has a coupon that will allow her to get ten percent off the discounted price. How much will Cara pay for the necklace if she uses the coupon?
At a sale, a necklace that was originally
Taking ten percent off of gives us ,
.
Taking ten percent off of this amount gives us
.
NOTE: This problem cannot be solved by taking twenty percent off of .
Taking ten percent off of
Taking ten percent off of this amount gives us
NOTE: This problem cannot be solved by taking twenty percent off of
Compare your answer with the correct one above
Matthew, Emily, Cynthia, John, and Stephanie are all running for student council. If three equivalent positions are available in this year's election, how many different leadership boards are possible?
Matthew, Emily, Cynthia, John, and Stephanie are all running for student council. If three equivalent positions are available in this year's election, how many different leadership boards are possible?
One possible approach is to enumerate all possibilities using initials for names (ie. MEC, MEJ, MES, etc). If we recognize that order does not matter in this problem, we can also enter into our calculators, and that will give us the answer of .
One possible approach is to enumerate all possibilities using initials for names (ie. MEC, MEJ, MES, etc). If we recognize that order does not matter in this problem, we can also enter
Compare your answer with the correct one above
Simplify.
Simplify.
When we are asked to simplify a matrix that is being multiplied by a constant we simply multiply each component of the matrix with the scalar factor that is on the outside of the matrix.
Therefore,
When we are asked to simplify a matrix that is being multiplied by a constant we simply multiply each component of the matrix with the scalar factor that is on the outside of the matrix.
Therefore,
Compare your answer with the correct one above