Question

1. if there are 4 swimmers in a race, in how many different orders can they finish (assuming there are no ties)?

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Explanation:

Step1: Identify the problem type

This is a permutation problem where we want to find the number of ways to arrange 4 swimmers in order. The formula for permutations of \( n \) distinct objects is \( n! \) (n factorial), which is \( n\times(n - 1)\times(n - 2)\times\cdots\times1 \). Here, \( n = 4 \).

Step2: Calculate the factorial

For \( n = 4 \), we calculate \( 4! \).
\( 4! = 4\times3\times2\times1 \)
First, \( 4\times3 = 12 \), then \( 12\times2 = 24 \), and \( 24\times1 = 24 \).

Answer:

\( 24 \)