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  • A committee of 3 members is to be formed from a group of 5 men and 4 women. In how many ways can the committee be formed if it must consist of 2 men and 1 woman, and one of the men must be the chai

A committee of 3 members is to be formed from a group of 5 men and 4 women. In how many ways can the committee be formed if it must consist of 2 men and 1 woman, and one of the men must be the chairperson of the committee?

 

Option: 1

160


Option: 2

320


Option: 3

270


Option: 4

120


Answers (1)

best_answer

To solve this, we can break it down into two parts:

1. Selecting the chairperson:

  • There are 5 men to choose from for the role of the chairperson.
  • So, we have 5 choices for the chairperson.

2. Selecting the remaining 2 members (1 man and 1 woman):

  • After selecting the chairperson, we have 4 men remaining and 4 women to choose from.
  • We need to select 1 man from the remaining 4 men and 1 woman from the remaining 4 women.
  • This can be done by calculating the combination of selecting 1 man from 4 men and 1 woman from 4 women.

\mathrm{C(4,1) \times C(4,1)=4 \times 4=16}

However, since one of the men must be the chairperson, members are selected. The chairperson can be selected be arranged in 2 ways (man-woman or woman-man).
To find the total number of ways to form the committee, chairperson, the number of ways to select the remain arrange the members within the committee:
Total number of ways =5 \times 16 \times 2=160

Therefore, the committee can be formed in 160 different ways if it must consist of 2 men and 1 woman, and one of the men must be the chairperson.

 

 

Posted by

Divya Prakash Singh

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