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

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

Answer 1

Answer: (C)

$108$

Total no. of balls in urn A $=3$

Total no. of balls in urn B $=9$

The number of ways in which two balls from urn A and two balls from urn B can be selected ${=}^3{C}_2{\times }^9{C}_2$

$=\frac{3!}{2!1!}\times \frac{9!}{2!7!}$

$=3\times 36$

$=108$