The Stamford High School basketball team has 3 new players this year. The new players can select from jerseys with numbers 1 through 8. In how many different ways could the new players be matched up with jerseys?
Question
The Stamford High School basketball team has 3 new players this year. The new players can select from jerseys with numbers 1 through 8. In how many different ways could the new players be matched up with jerseys?
Solution
This is a permutation problem. The formula for permutations is nPr = n! / (n - r)!. In this case, n is the number of jerseys (8) and r is the number of new players (3).
Step 1: Calculate n! (factorial of n). This is 8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40320.
Step 2: Calculate (n - r)!. This is (8 - 3)! = 5! = 5 * 4 * 3 * 2 * 1 = 120.
Step 3: Divide n! by (n - r)!. This is 40320 / 120 = 336.
So, the new players could be matched up with jerseys in 336 different ways.
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