Question

There are two urns. Urn $A$ has $3$ distinct red balls and urn $B$ has $9$ distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done, is equal to?

• A. $3$
• B. $36$
• C. $66$
• D. $108$

Answer 1

The correct option is D

$108$

Explanation for the correct answer:

Compute the number of ways:

The number of ways two balls can be chosen from Urn $A$$={}^{3}C_2$

The number of ways two balls can be chosen from Urn $B$ $={}^{9}C_2$

Thus the transfer of two balls from the urns can be made in total ways $={}^3{C}_2\times {}^9{C}_2$

$=\frac{3!}{2!}\times \frac{9!}{2!7!}$

$=3\times 36$

$=108$

Hence, two balls can be transferred from the urns in $108$ ways.

Hence, option $\left(D\right)$ is the correct answer.