in a soccer match a tie at the end of two overtime periods leads to a shootout with five kicks taken by each team from the penalty mark. each kick must be taken by a different player. how many ways can 5 players be selected from 11

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donnabridgman1940 donnabridgman1940

08-11-2022
Mathematics

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in a soccer match a tie at the end of two overtime periods leads to a shootout with five kicks taken by each team from the penalty mark. each kick must be taken by a different player. how many ways can 5 players be selected from 11

Answer :

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tutorconsortium270 tutorconsortium270 · Answer 1 · 2022-11-12T02:10:50-05:00

The number of ways that 5 players can be selected from the 11 eligible players is; 462 ways

The number of ways that the 5 selected players can they be designated as first, second, third, fourth, and fifth is; 120 Ways

What is Permutations and Combinations ?

Permutations and combinations are ways of representing groups of objects by selecting them and sub-setting them into sets. It defines different ways of arranging a particular data group. When we choose data or objects from a particular group, it is called a permutation and the order in which they are presented is called a combination. Both concepts are very important in mathematics.

Calculation

We are given that In a soccer match;

A tie at the end of two overtime periods leads to a "shootout" with five kicks taken by each team from the penalty mark.

Each kick must be taken by a different player

Now, to find the number of ways that 5 players can be selected from the 11 eligible players, we will use combination to get;

11C5 = 11!/(5! * (11 - 5)!)

= 11!/(5! * 6!)

= 462 ways

Now, if we care about order or position, we will use permutation to get the number of ways that the 5 selected players can they be designated as first, second, third, fourth, and fifth;

5P5 = 5!/(5 - 5)

= 120 Ways

learn more about Permutations and Combinations at; brainly.com/question/4658834

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