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  • How many different ways are there to select a committee of 4 men and 3 women out of a pool of 7 men and 9 women?  Option: 1

How many different ways are there to select a committee of 4 men and 3 women out of a pool of 7 men and 9 women?

 

Option: 1

1840

 

 


Option: 2

2225 


Option: 3

3420


Option: 4

2940

 

 


Answers (1)

best_answer

We have to choose 4 men out of 7 men.

This can be done in {}^7C_4  ways.

Thus,

\begin{aligned} & { }^7 C_4=\frac{7 !}{4 !(7-4) !} \\ & { }^7 C_4=\frac{7 !}{4 ! 3 !} \\ & { }^7 C_4=\frac{7 \times 6 \times 5 \times 4 \times 3 \times 2}{4 \times 3 \times 2 \times 3 \times 2} \\ & { }^7 C_4=35 \end{aligned}

We have to choose 3 women out of 9 women.

This can be done in {}^9C_3 ways.

\begin{aligned} &{ }^9 C_3=\frac{9 !}{3 !(9-3) !}\\ &{ }^9 C_3=\frac{9 !}{3 ! 6 !}\\ &{ }^9 C_3=\frac{9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2}{3 \times 2 \times 6 \times 5 \times 4 \times 3 \times 2}\\ &{ }^9 C_3=84 \end{aligned}

The total number of ways is 35 \times 84 =2940.

Therefore, the number of ways committees have been chosen in 2940 ways.

 

Posted by

Deependra Verma

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