Question

A bag of contains 6 white marbles and 5 red marbles. Find the number of ways in which four marbles can be drawn from the bag if they can be of any color.

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{marbles}=6+5=11 \\ \mathrm{Marbles}\mathrm{to}\mathrm{select}=4 \\ \mathrm{Number}\mathrm{of}\mathrm{ways}\mathrm{to}\mathrm{select}4\mathrm{marbles}={}^{11}\mathrm{c}_4 \\ =\frac{11!}{4!7!}=\frac{11\times 10\times 9\times 8\times 7!}{4\times 3\times 2\times 1\times 7!} \\ =\frac{11\times 10\times 9\times 8}{8\times 3}=330\mathrm{ways}\mathrm{ANS}... \end{gathered}$$

Regards