Question

In how many ways can a committee of 1 man and 3 women can be formed from a group of 3 men and 4 women?

Answer 1

$Number \:of \:men \: in \: a \: group = 3 \\Number \: of \:women \: in \:the \: group = 4$

$Number \:of \:ways \: a \:committee \:of \\1 \:man \: and \: 3 \:women \: can \: be \: formed \\from \: a \: group \:of \: 3 \:men \:and \:4 \:women \\= ^{3}C_{1} \times ^{4}C_{3} \\= \frac{3!}{(3-1)! 1! } \times \frac{4!}{(4-3)! 3! }$

$\boxed {\pink { ^{n}C_{r} = \frac{n!}{(n-r)! r! }}}$

$= \frac{3!}{2! \:1! } \times \frac{4!}{1! 3! }$

$=\frac{3\times 2!}{2! \:1! } \times \frac{4\times 3!}{1! 3! }$

$= 3 \times 4\\= 12$

Therefore.,

$\red { Number \:ways }\green {= 12}$

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Answer 2

Answer:

Hope it will help you!..........