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}=(15!)/(3!12!)\cdot(5!)/(2!3!)=(13\cdot14\cdot15)/(2\cdot3)\cdot(4\cdot5)/(2)=13\cdot7\cdot5\cdot2\cdot5=4550`