(10 points) From a group of 9 men and 7 women a committee consisting of 4 men and 4 women is to be formed. How many different committees are possible if (a) 2 of the men refuse to serve together? (a) 2 of the women refuse to serve together? (a) 1 man and 1 woman refuse to serve together?

a) 2450

b) 1890

c) 1050

Step-by-step explanation:

Given:

- Available Group = 9 M & 7 F

- Committee of= 4 M and 4 W to be formed

Find:

- (a) 2 of the men refuse to serve together?

- (a) 2 of the women refuse to serve together?

- (a) 1 man and 1 woman refuse to serve together?

Solution:

- The question pertains to a selection process, We will use combinations for each case as follows.

part a)

- Since 2 men cant be selected together. Then we have to discount for one man while selecting Man for the committee. Hence, the combinations are:

                                   8C4 x 7C4 = 2450

part b)

- Since 2 women cant be selected together. Then we have to discount for one woman while selecting them for the committee. Hence, the combinations are:

                                   9C4 x 6C4 = 1890

part b)

- Since 1 women and a man cant be selected together. Then we have to discount for one woman and one man while selecting them for the committee. Hence, the combinations are:

                                   8C4 x 6C4 = 1050

y= -

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: