SravnaTestPrep wrote:
Less than half of a committee that is to be formed out of certain group, are to be men. If there are 100 possible ways of forming the committee, then the number of men in the committee can be,
A. 2
B. 3
C. 4
D. 5
E. cannot be determined
1. Let there be m men and w women out of which the committee is formed.
2. mCn * wCr = 100, where n is the number of men chosen and r is the number of women chosen
3. The possible products for LHS of (2) are, 100 * 1, 50 * 2, 25 * 4, 20 * 5, 10 * 10
4. Since the number of women is greater than the number of men, the first three products in (3) can be rejected as they would not satisfy this condition.
5. In the case of the fourth product, 20 * 5 may be given by 6C3 * 5C1. Though this may satisfy the condition with 3 women and 1 man, 1 man is not in the choices given.
6. The last product 10 * 10 may be given by 5C2 * 5C3 with 2 men and 3 women. This satisfies the condition and also 2 men is one of the choices given.
Therefore the answer is choice A.
could not understand that y these 3 products r not satisfying the condition.
as 100*1 can mean that there are 100 women and 1 man....50*2 means that 50 women and 2 men....25*4 means that 4 men 25 women.....
my other concern is how to calculate quickly that 20 is 6C3 or 10 is 5C2.