A performing arts center is holding elections for the new board of directors. If there are 4 different positions open on the board and 5 people want to be considered, how many different ways are there to fill the positions?
Question
A performing arts center is holding elections for the new board of directors. If there are 4 different positions open on the board and 5 people want to be considered, how many different ways are there to fill the positions?
Solution
This is a problem of permutations. In permutations, the order of selection matters.
Here are the steps to solve this problem:
Step 1: Identify the number of total options and the number of positions. In this case, there are 5 people who want to be considered for 4 positions.
Step 2: Use the formula for permutations, which is nPr = n! / (n - r)!, where n is the total number of options, r is the number of positions, and "!" denotes factorial.
Step 3: Plug the numbers into the formula. So, we have 5P4 = 5! / (5 - 4)!
Step 4: Calculate the factorials. 5! = 5 * 4 * 3 * 2 * 1 = 120 and (5 - 4)! = 1! = 1.
Step 5: Divide the two factorials. 120 / 1 = 120.
So, there are 120 different ways to fill the 4 positions on the board of directors from the 5 people who want to be considered.
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