Question

A committee of five people is to be chosen from a club that boasts a membership of 10 men and 12 women. a) How many ways the committee can be formed if it is to contain at least two women? b) How many ways

Answer 1

the first problem is you need to include at least 2 women.
this means you can include 2 women or 3 women or 4 women or 5 women on the committee since there is no requirement on the number of males that have to be on the committee.
if 3 men and 2 women are on the committee, then the possible number of combinations is c((10,3) * c(12,2) which is equal to 7920.

if 2 men and 3 women are on the committee, then the possible number of combinations is c(10,2) * c(12,3) which is equal to 9900.

if 1 man and 4 women are on the committee, then the possible number of combinations is c(10,1) * c(12,4) which is equal to 4950.

if no men and 5 women are on the committee, then the possible number of combinations is c(10,0) * c(12,5) which is equal to 792.


you would need to add these up to get the total number of possible combinations.

7920 + 9900 + 4950 + 792 = 25362

Answer 2

the answer of the question is 16.
women. men. committee. ways
2. 3. 5. 2×3=6
3. 2 5. 3×2=6
4. 1. 5. 4×1=4
5. 0. 5. 5×0=0
the ways are= 6+6+4+0=16