In how many ways a commitee of six members be formed from 7 men and 5 women if that commitee contains at least 2 women?

(5 C 2 \times 7 C 7) + (5 C 3 \times 7 C 3) + (5 C 4 \times 7 C 2) + (5 C 5 \times 7 C 1)

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(5 C 2 \times 7 C 4) + (5 C 3 \times 7 C 3) + (5 C 2 \times 7 C 2) + (5 C 5 \times 7 C 2)

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(5 C 2 \times 7 C 4) + (5 C 3 \times 7 C 3) + (5 C 4 \times 7 C 2) + (5 C 5 \times 7 C 1)

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(5 C 2 \times 7 C 4) + (5 C 3 \times 7 C 4) + (5 C 2 \times 7 C 2) + (5 C 5 \times 7 C 1)

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Solution

The correct option is C $(5 C 2 \times 7 C 4) + (5 C 3 \times 7 C 3) + (5 C 4 \times 7 C 2) + (5 C 5 \times 7 C 1)$
At least two women means two or more than two women-
four cases will be possible
Case 1 - exactly two women are selected
$(5 C 2 \times 7 C 4)$
Case 2 - exactly three women are selected
$(5 C 3 \times 7 C 3)$
Case 3 - exactly four women are selected $(5 C 4 \times 7 C 2)$
Case 4 - exactly five women are selected $(5 C 5 \times 7 C 1)$
adding all will give total ways possible
option (c) is correct

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