Question

There are $12$ different marbles to be divided between two children in the ratio $1:2$. The number of ways it can be done -

• A. 990
• B. 495
• C. 600
• D. none

Answer 1

The correct option is A 990

Dividing $12$ marbles into $1:2$ ratio

$=$ choosing $4$ marbles out of $12$

(then ratio $\frac{4}{8}=\frac{1}{2}$)

Choosing $4$ marbles can be done in ${}^{12}{C}_4$ ways giving those $4$ marbles to any kid can be done is $2$ ways

$\therefore$ Required no of ways $={}^{12}{C}_4\times 2$

$=\frac{12!}{8!\times 4!}\times 2$

$=\frac{\mathrm{12.11.10.9}}{\mathrm{4.3.2.1}}\times 2$

$=990$ ways.