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ACT Math : How to find combinations with a matrix

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Example Question #1 : How To Find Combinations With A Matrix

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?

Possible Answers:

125

Correct answer:

Explanation:

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 5 nCr 3 into our calculators, and that will give us the answer of .

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Example Question #2582 : Act Math

Simplify.

$3\cdot \begin{bmatrix} 2 & 6 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix}18 & 6 \end{bmatrix}$

$\begin{bmatrix}6 & 6 \end{bmatrix}$

$\begin{bmatrix}6 & 2 \end{bmatrix}$

$\begin{bmatrix}6 & 18 \end{bmatrix}$

$\begin{bmatrix}2 & 18 \end{bmatrix}$

Correct answer:

$\begin{bmatrix}6 & 18 \end{bmatrix}$

Explanation:

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,

$3\cdot \begin{bmatrix} 2 & 6 \end{bmatrix} \rightarrow \begin{bmatrix} 3\cdot 2 & 3\cdot 6 \end{bmatrix}=\begin{bmatrix} 6 & 18 \end{bmatrix}$

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Example Question #3 : How To Find Combinations With A Matrix

At a sale, a necklace that was originally $\$120$ 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?

Possible Answers:

$\$96$

$\$97.20$

$\$96.60$

$\$100.40$

$\$100$

Correct answer:

$\$97.20$

Explanation:

Taking ten percent off of $\$120$ gives us $\$108$ ,

$120\cdot (1-0.10)=120\cdot 0.90=108$ .

Taking ten percent off of this amount gives us $\$97.20$

$108 \cdot (1-0.10)=108\cdot (0.90)=97.20$ .

NOTE: This problem cannot be solved by taking twenty percent off of $\$120$ .

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ACT Math : How to find combinations with a matrix

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : How To Find Combinations With A Matrix

Example Question #2582 : Act Math

Example Question #3 : How To Find Combinations With A Matrix

All ACT Math Resources

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