A committee of 3 ladies and 4 gents is to be formed out of 8 ladies and 7 Gents mrs X refuses to serve in a committee in which Mr y is member. the number of such commitees is
Answers
Let us first form a committee with 3 ladies and 4 gents.
>>7C4*8C3 =7C4= 7*6*5 / 3*2*1 = 35
8C3 = 8*7*6/3*2*1 = 56
We get 56*35 = 1960
Let us calculate the possibility when
Mrs.X and Mr. Y are together.
>>6c3*7c2 = 6c3 = 6*5*4/3*2*1 = 20
7c2= 7*6/2*1 = 21
We get 20 * 21 = 420
thus, 1960-420 = 1540
Given : committee of 3 ladies and 4 gents is to be formed out of 8 ladies and 7 Gents So That Mrs .X And Mr.Y do not Come together
To Find : Total Number of Committees which can be formed
Solution:
Total = 7 Men and 8 Women
Committee to be formed
4 Men and 3 Women
3 Women out of 8 Women can be selected in ⁸C₃ = 56 ways
4 Men out of 7 Men can be selected in ⁷C₄ = 35 ways
Total = 56 x 35 = 1960
Mrs.X And Mr.Y can not be together
Cases when X & Y are Selected
Then remaining 2 Women out of 7 Women can be selected in in ⁷C₂ = 21 Ways
Then remaining 3 Men out of 6 men can be selected in in ⁶C₃ = 20 Ways
X & Y are together = 21 x 20 = 420
When X & Y are not together then 1960 - 420 = 1540 Ways
Total Ways committee can be formed = 1540 ways
in 1540 ways committees can be formed of 4 Men And 3 Women From 7 Men And 8 Women So That Mrs.X And Mr.Y Do Not Come together
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