Respuesta :
There are 5040 different ways can the runners finish first, second, third, and fourth place if ten runners are racing.
What is the permutation?
The permutation is defined as considered an ordered combination.
The general formula for this is:
P(n, r) = n! (n-r)!
Ten runners are racing
There are ten runners who can win first place, hence there are ten ways.
Any of the remaining 9 runners may get up to the second position in nine different ways.
Any of the remaining 8 runners may get up to the third position in eight different ways
Any of the remaining 7 runners may get up to the fourth position in seven different ways
So total number of ways = 10 × 9 × 8 × 7 = 5040
Another way 4 Out of 10 need to select where order matters
= ¹⁰P₄
= 10!/6!
= 10 × 9 × 8 × 7
= 5040
Hence, there are 5040 different ways can the runners finish first, second, third, and fourth place if ten runners are racing.
Learn more about the permutations here:
https://brainly.com/question/1216161
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