Question

A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if two must be white and two red.

Answer 1

Given : A bag contains $6$ white and $5$ red marbles.

We have to select $2$ white marbles and $2$ red marbles from $6$ white and $5$ red marbles.

Hence required number of ways

$={}^6{C}_2\times {}^5{C}_2$

$=\frac{6!}{(2!)\left(4\right)!}\times \frac{5!}{(2!)\left(3\right)!}$

$=\frac{6\times 5\times (4!)}{(2\times 1)(4!)}\times \frac{5\times 4\times (3!)}{(2\times 1)(3!)}$

$=150$