Out of 7 gents and 4 ladies a committee of 5 is to be formed. The number of committees
such that each committee includes at least one lady is
(a) 400
(b) 440
(c) 441
(d) none of these
Answers
Answered by
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441
it has four cases
case 1
4 gents and 1 lady
7C4x4C1
= 35×4
=140
case 2
3 gents and 2 ladies
7C3×4C2
= 35*6
=210
case 3
2 gents and 3 ladies
7C2×4C3
=21×4
=84
case 4
1 gent and 4 ladies
7C1*4C4
=7*1
=7
Ans
number of committees=140 + 210 + 84 + 7 =441
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