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Answer :
The number of different permutations for the places in which the 6 runners can finish is 720.
To calculate the number of permutations of 6 distinct objects. A permutation is an arrangement of items in a specific order, and the formula to find the total number of permutations of 'n' distinct objects is given by n!. Here, n=6 since there are 6 runners.
The formula for permutations is:
[tex]n! = n \times (n-1) \times (n-2) \times \cdots \times 1[/tex]
For 6 runners, this would be:
[tex]6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1[/tex]
Calculating this step-by-step:
- [tex]6 \times 5 = 30[/tex]
- [tex]30 \times 4 = 120[/tex]
- [tex]120 \times 3 = 360[/tex]
- [tex]360 \times 2 = 720[/tex]
- [tex]720 \times 1 = 720[/tex]
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