In how many ways can a committee be formed of 5 members from 6 men and 4 women if the committee has at least one woman

186

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246

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252

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None of these

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Solution

The correct option is B 246
The number of ways can be deduce as follows :
1 woman and 4 men $=^{4} C_{1} \times^{6} C_{4} = 60$
2 women and 3 men $=^{4} C_{2} \times^{6} C_{3} = 120$
3 women and 2 men $=^{4} C_{3} \times^{6} C_{2} = 60$
4 women and 1 man $=^{4} C_{4} \times^{6} C_{1} = 6$
Required number of ways 60 + 120 + 60 + 6 = 246.

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In how many ways can a committee be formed of 5 members from 6 men and 4 women if the committee has at least one woman

The correct option is B 246The number of ways can be deduce as follows : 1 woman and 4 men =4C1×6C4=60 2 women and 3 men =4C2×6C3=120 3 women and 2 men =4C3×6C2=60 4 women and 1 man =4C4×6C1=6 Required number of ways 60 + 120 + 60 + 6 = 246.