The Weston High School soccer team has 5 new players this year. If there are 2 different starting positions open, in how many ways can these positions be assigned to the new players? ways
Question
The Weston High School soccer team has 5 new players this year. If there are 2 different starting positions open, in how many ways can these positions be assigned to the new players? ways
Solution
This is a problem of permutations.
Step 1: Identify the number of items to choose from. In this case, we have 5 new players.
Step 2: Identify the number of positions to fill. In this case, we have 2 starting positions.
Step 3: Use the formula for permutations, which is nPr = n! / (n - r)!. In this case, n is the number of items to choose from (5 players) and r is the number of positions to fill (2 positions).
Step 4: Calculate the factorial of n, which is 5! = 5 * 4 * 3 * 2 * 1 = 120.
Step 5: Calculate the factorial of (n - r), which is (5 - 2)! = 3! = 3 * 2 * 1 = 6.
Step 6: Divide the factorial of n by the factorial of (n - r) to get the number of permutations. In this case, 120 / 6 = 20.
So, there are 20 different ways the 2 starting positions can be assigned to the 5 new players.
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