In a race between 18 people, how many ways can the top 5 finishers be arranged?
1 answer:
Answer:
Step-by-step explanation:
This is permutation, since order matters. The formula for us is
₁₈P₅ = which simplifies to
₁₈P₅ =
The factorial of 13 cancels out on the top and bottom leaving you with
₁₈P₅ = 18 × 17 × 16 × 15 × 14
which comes to 1,028,160 ways
Another way to look at it is: the first 5 people of 18 finish and the others you don't care about. Once the first place person is first, there are only 4 of the 18 left to finish in second place. Then there are only 3 left to finish in third place, etc. So if we use that reasoning, we don't even need to use the formula, we can just say
18 * 17 * 16 * 15 * 14 and those are the first 5 people of 18 to finish.
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