Home
Class 12
MATHS
A committee of 6 is chosen from 10 men a...

A committee of 6 is chosen from 10 men and 7 women so as to contain at least 3 men and 2 women. In how many ways can this be done if two particular women refuse to serve on the same committee? a. 850 b. 8700 c. 7800 d. none of these

Text Solution

Verified by Experts

The correct Answer is:
7800
We have 10 men and 7 women and a committee of 6 containing at least 3 men and 2 women is to be formed.

Now, let us consider the case when 2 particular women are always there in the same committee. We have to make a selection of 4 from 10 men and 5 women. In this case, to comply with the initial condition of at least 3 men and at least 2 women, we have the following cases :

Hence, the number of committees when two particular women are never together is 8610-810=7800.
Promotional Banner

Similar Questions

Explore conceptually related problems

In how many ways can 7 men be slected from 16 men so that 4 particular men will not be there ,

A committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done ? How many of these committees would consist of 1 man and 2 women ?

A committee of 12 is to be formed from nine women and eight men. In how many ways can this be done if at least five women have to be included in a committee? In how many of these committees a. the women hold majority? b. the men hold majority?

A committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done? How many of these committees would consist of 1 man and 2 women?

A committee of 5 is to be formed from 9 women and 8 men. if the committee commands women's majority, then find the number of ways this can be done ?

A committee of 5 is to be formed from six ladies and four gentlemen . In how many ways this can be done so that the committee contains at least two ladies,

A committee of 5 is to be formed from six ladies and four gentlemen . In how many ways this can be done so that the committee contains exactly two ladies ,

A committee of 5 is to be formed from six ladies and four gentlemen . In how many ways this can be done so that the committee contains at most two ladies ?

The number of ways of choosing a committee of two women and three men from five women and six men, if Mr. A refuses to serve on the committee if Mr. B is a member and Mr. B can only serve if Miss C is the member of the committee is a. 60 b. 84 c. 124 d. none of these

In a group of boys, two boys are brothers and six more boys are present in the group. In how many ways can they sit if the brothers are not to sit along with each other? a. 2xx6! b. ^7P_2xx6! c. ^7C_2xx6! d. none of these