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Question
In how many ways can a committee of 5 persons be formed out of 6 men and 4 women when at least one woman has to be necessarily selected?
Solution
5 persons are to be selected out of 6 men and 4 women. At least, one woman has to be selected in all cases.
\[\text{Required number of ways} =^4 C_1 \times^6 C_4 + {}^4 C_2 \times^6 C_3 + {}^4 C_3 \times^6 C_2 +^4 C_4 \times^6 C_1 \]
\[ = 60 + 120 + 60 + 6 \]
\[ = 246\]
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