Out of 5 women and 4 men, a committee of three members is to be formed in such a way that atleast one member is a woman. In how many different ways can it be done?
A
80
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B
84
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C
76
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D
96
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E
None of these
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Solution
The correct option is A 80
The committee will be formed as follows (i) 1 woman and 2 men (ii) 2 women and 1 man (iii) 3 women. ∴ Required number of committees =5C1×4C2+5C2×4C1+5C3=5×4×31×2+5×41×2×4+5×4×31×2×3 = 30 + 40 + 10 = 80