Answer:
(a) Number of committees formed if there are no restrictions = 350
(b) Number of committees formed if 2 of the women refuse to serve together = 310
Step-by-step explanation:
As per the question,
Number of women = 7
Number of men = 5
The different committees are possible if
(a) There are no restrictions
Number of committees formed
= [tex]^{7}C_{4} \times ^{5}C_{3}[/tex]
= 350
(b) 2 of the women refuse to serve together
From the 350, we must subtract the number of ways those two women serve together.
If the men and women both serve together, then 1 woman serve with 4 men.
The men are chosen
[tex]=^{5}C_{3} = 10\ ways[/tex],
So
The number we must subtract from the 350 is 4 × 10 = 40
∴ Number of committees formed = 350 - 40 = 310.
