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 they must all be of the same colour

Answer 1

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

If all the $4$ marbles are of the same color, choose $4$ from $6$ white or choose $4$ from $5$ red.

Hence required number of ways

$={}^6{C}_4+{}^5{C}_4$

$=\frac{6!}{(4!)\left(2\right)!}+\frac{5!}{(4!)\left(1\right)!}$

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

$=20$