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Question
In how many ways can a committee of 5 be made out of 6 men and 4 women containing at least one women?
Options
246
222
186
none of these
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Solution
246
\[\text{Required number of ways} =^4 C_1 \times {}^6 C_4 +^4 C_2 \times {}^6 C_3 +^4 C_3 \times {}^6 C_2 +^4 C_4 \times {}^6 C_1 \]
\[ = 60 + 120 + 60 + 6 \]
\[ = 246\]
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