Question

There are 20 students 15 men and 5 women in a maths class,in how many different ways can a committee of 3 men and 2 women be choosen
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Answer 1

$\displaystyle\\\binom{15}{3}\cdot\binom{5}{2}=\dfrac{15!}{3!12!}\cdot\dfrac{5!}{2!3!}=\dfrac{13\cdot14\cdot15}{2\cdot3}\cdot\dfrac{4\cdot5}{2}=13\cdot7\cdot5\cdot2\cdot5=4550$