In a race with eight swimmers, how many ways can the swimmers finish first, second and third?
Question
In a race with eight swimmers, how many ways can the swimmers finish first, second and third?
Solution
This is a permutation problem.
Step 1: Identify the number of total items. In this case, we have 8 swimmers.
Step 2: Identify the number of positions to fill. In this case, we have 3 positions (first, second, and third).
Step 3: Use the formula for permutations, which is nPr = n! / (n - r)!. In this case, n is the total number of items (8 swimmers) and r is the number of positions to fill (3 positions).
Step 4: Calculate the factorial of n (8!). This is 8765432*1 = 40320.
Step 5: Calculate the factorial of (n - r) which is (8 - 3)!. This is 54321 = 120.
Step 6: Divide the factorial of n by the factorial of (n - r). This is 40320 / 120 = 336.
So, there are 336 different ways the swimmers can finish first, second, and third.
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