Hence, 15 people out of 3 people can be chosen in 35 ways.
Combinations:
- It is a method that helps us to determine the number of possible ways an item can be chosen given that the order of selection does not matter.
- Hence we are free to select the items in any order.
- Combinations are often confused with permutations. Permutations are the number of ways the given items can be arranged. Here the order is important.
The formula for combinations:
- If we have 'n' items and we are required to choose 'r' items, the number of ways in which it can be done is calculated as:
- [tex]^{n}C_{r} }[/tex] = [tex]\frac{n!}{(n-r)!r!}[/tex]
It is given that:
The total number of people in a race, n = 15
The number of finalists, r = 3.
Hence, the number of ways in which 3 people out of the 15 people can be finishers are:
[tex]^{15}C_{3} }[/tex] = [tex]\frac{15!}{(15-3)!3!}[/tex] = [tex]\frac{15!}{12!3!}[/tex] = 35.
Hence, 15 people out of 3 people can be chosen in 35 ways.
For similar questions on permutations and combinations, visit:
https://brainly.com/question/13387529?referrer=searchResults
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