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A committee of 7 has to be formed from 9 boys and 4 girls.In how many ways can this be done when the committee consists of A committee having at least 3 girls will consists of (a) 3 girls 4 boys (b) 4 girls 3 boys

$\begin{array}{1 1}(A)\;504\\(B)\;508\\(C)\;588\\(D)\;590\end{array} $

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This can be done in $4C_3\times 9C_4+4C_1\times 9C_3$ ways
$\Rightarrow \large\frac{4}{1}\times \frac{9\times 8\times 7\times 6}{1\times 2\times 3\times 4}$$+1\times \large\frac{9\times 8\times 7}{1\times 2\times 3}$ ways
$\Rightarrow 504+84$
$\Rightarrow 588$ ways
Hence (C) is the correct answer.
answered May 14, 2014 by sreemathi.v

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