(Q). Out of 8 men and 4 women a committee of 5 is to be formed. In how many ways this can be done:
(i). So as to include at least 1 woman in the committee
(ii). So as to include at least 1 woman in the comittee & exclude at least 1 man from the committee.
Solution:-
(i).
Method(1):-
Hence required number of ways
= 280 + 336 + 112 + 8
= 736 Answer
Method(2):
Total number of ways to select he committee without any restriction = ¹²C₅
total number of way when no woman is selected i.e. all 5 are men = ⁸C₅
Hence required number of ways = ¹²C₅ – ⁸C₅
= 736 Answer
(ii)
Here also possible cases are same as the cases in (i).
Hence number of ways = ⁴C₁×⁸C₄ + ⁴C₂×⁸C₃ + ⁴C₃×⁸C₂ + ⁸C₁×⁴C₄
= 736 Answer