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How many committees of five people can be chosen from 20 men and 12 women such that each committee contains at least three women

1. 75240
2. 52492
3. 41800
4. 9900

Total 5 people need to be chosen with condition that at least 3 must be women and no restriction on men

For that, we have 20 men and 12 women

Case 1: Take 2 men from 20 men and 3 women from 12 women

20C * 12C3

Case 2: Take 1 man from 20 men and 4 women from 12 women

20C* 12C4

Case 3: Take 0 man from 20 men and 5 women from 12 women

20C* 12C5

All these 3 cases are mutually exclusive:

ANS= 20C * 12C +  20C* 12C +  20C* 12C5

ANS=52492

by

Can u plz explain what is C???
c means combination.

nCr=n!/(n-r)!.r!
Are there any shortcuts? this is a tedious way of doing it.