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  • How many different ways are there to select the president and vice-president from a committee of 5 people, presuming that no one person can hold both positions?<div class='qna-option'

How many different ways are there to select the president and vice-president from a committee of 5 people, presuming that no one person can hold both positions?

Option: 1

20


Option: 2

15


Option: 3

16

 


Option: 4

12


Answers (1)

best_answer

There are 5 different individuals, and we must choose 2 of them to form a committee. Repetition is not permitted (one individual is not permitted to hold more than one position).

As a result, as many committees as there are possible combinations of 5 people taken two at a time can be formed.

This is given by,

^{5}P_{2}=\frac{5!}{(5-2!)}

^{5}P_{2}=\frac{5!}{(3!)}

^{5}P_{2}=20
Therefore, the number of ways to choose a president and a vice president is 20.

Posted by

manish painkra

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