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  • A committee of at least three members is to be formed from a group of 6 boys and 6 girls such that it always has a boy and a girl.The number of ways to form such a committee is<div class='qna-o

A committee of at least three members is to be formed from a group of 6 boys and 6 girls such that it always has a boy and a girl.The number of ways to form such a committee is

Option: 1

2^{11}-2^{6}-13


Option: 2

2^{12}-2^{7}-35


Option: 3

2^{11}-2^{7}-35


Option: 4

2^{12}-2^{7}-13


Answers (1)

best_answer

Required number of ways

\mathrm{= \left({ }^{6} C_{1}+{ }^{6} C_{2}+\cdots+{ }^{6} C_{6}\right)\left({ }^{6} C_{1}+{ }^{6} C_{2}+\cdots\right.\left.{ }^{6} C_{6}\right)-\left({ }^{6} C_{1}\right)\left({ }^{6} C_{1}\right)}
\mathrm{= \left(2^{6}-1\right)\left(2^{6}-1\right)-36=2^{12}-2^{7}-35}

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shivangi.bhatnagar

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