Algebra II : Algebra II
Study concepts, example questions & explanations for Algebra II
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Example Questions
Example Question #2 : Permutations
7 students try out for the roles of Starsky and Hutch in a new school production. How many different ways can these roles be cast?
There are 7 potential actors and 2 different roles to fill. This would be calculated as 
Example Question #3 : Permutations
How many different 4 letter words can be made out of the letters A, B, C, D, and E?
Since order matters, use the permutation formula:
There are 5 letters to choose from (n), and you pick 4 of them (r).
So there are 120 possible words that can be formed.
Example Question #11 : Permutations
The soccer team awards gold, silver, and bronze trophies for the top three goal scorers over the season. If the soccer team has 11 players, how many different ways could the gold, silver, and bronze trophies be awarded?
Because the order is important, this is a permutation. There are 11 players to fill 3 spots, so 
Example Question #12 : Permutations
How many possible ways can the letters A and B be assigned to nine people?
Write the formula for permutation.
Evaluate 
Cancel all the common terms in the numerator and denominator.
The answer is:
Example Question #13 : Permutations
Evaluate:
Write the permutation formula.
Substitute the values in the given problem.
Cancel out the terms in the numerator and denominator.
The remaining terms in the numerator are:
The answer:
Example Question #51 : Probability
Evaluate:
Write the permutation formula.
Substitute the values of the variables.
Simplify the factorials.
Cancel the common terms.
The answer is:
Example Question #15 : Permutations
Determine the value of:
Write the permutation formula.
Substitute the values of 
Expand the terms.
Cancel out the terms in the denominator and denominator.
The remaining terms are:
Multiply these numbers.
The answer is:
Example Question #16 : Permutations
Solve the permutation:
Write the formula for permutation.
Substitute the values and expand the factorials.
Reduce the terms.
The answer is:
Example Question #17 : Permutations
Suppose a locksmith designs a three digit lock with numbers ranging only from zero to five. What is the number of permutations possible?
The formula to determine the permutation is:
Notice that for each number, there are 6 different choices since we have numbers ranging from zero to five, not five.
For a three digit lock, 
Substitute the terms into the formula.
The answer is:
Example Question #18 : Permutations
There are 
This is a permutation of 10 objects (runners) taken 3 at a time, with no replacements.
Another way to look at this would be there are 10 runners competing for 1st place, 9 runners competing for 2nd place, and 8 runners competing for 3rd place.
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