Question

If 25 people start a race, in how many different ways can the top 2 finishers be determined?

Answer 1

There are total 600 number of ways or  permutations the top two finishers can be determined.

According to the given question.

Total number of people who are participating in a race = 25

In 25 participants the total number of participants to be selected to finish the race = 2

As we know that "a permutation is a mathematical calculation of the number of ways a particular set can be arranged, where the order of the arrangement matters". Which can be calculated as

$^{n}P_{r} = \frac{n!}{(n-r)!}$

Where,

$^{n} P_{r}$ is the number of permutations

n is the total number of objects

r is the numbers of objects to be selected

Thereofore,

The total number of ways, or permutaions the two top finishers can be determined is given by

$^{25} P_{2}$

= 25!/(25-2)!

= 25!/23!

= 25 × 24 × 23!/23!

= 25 × 24

= 600

Hence, there are total 600 ways or number of permutations the top two finishers can be determined.

Find out more information about permutations or number of ways  here:

brainly.com/question/28021983

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