Question

10. (1) An executive committee of 6 is to be formed from 4
ond
ladies and 7 gentlemen. In how many ways can this be
formed when the committee contains (a) only 2 lady l 22. Pro
members (b) at least 2 lady members?
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Answer 1

Answer:

Total 8 gentlemen & 5 ladies.

Committee to be of 6 members & should contains at least 3 ladies.

First assumption:

If there are 3 ladies in committee then possibilities are= 5c3 * 8c3 = (5*4*3/3*2*1) * (8*7*6/3*2*1)= 10* 56= 560

Second assumption:

If there are 4 ladies in committee then possibilities are= 5c4 * 8c2 = (5*4*3*2/4*3*2*1) * (8*7/2*1)=5* 28= 140

Third assumption:

If there are 5 ladies in committee then possibilities are= 5c5 * 8c1 = (5*4*3*2*1/5*4*3*2*1) * (8/1)=1* 8= 8

So total possibilities of a committee contains at least 3 ladies are= 560+140+8= 708.