There are two urns. Urn A has 3 distinct red | vedclass

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(C) Total number of balls in urn $A = 3$.Total number of balls in urn $B = 9$.We need to select $2$ balls from urn $A$ and $2$ balls from urn $B$ to t

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$108$

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(C) Total number of balls in urn $A = 3$.Total number of balls in urn $B = 9$.We need to select $2$ balls from urn $A$ and $2$ balls from urn $B$ to transfer them to the other urn.The number of ways to select $2$ balls from $3$ distinct balls in urn $A$ is given by $^3C_2$.$^3C_2 = \frac{3!}{2!1!} = 3$.The number of ways to select $2$ balls from $9$ distinct balls in urn $B$ is given by $^9C_2$.$^9C_2 = \frac{9!}{2!7!} = \frac{9 	imes 8}{2 	imes 1} = 36$.Since these selections are independent,the total number of ways to perform the transfer is the product of the two individual selection counts.Total ways $= ^3C_2 	imes ^9C_2 = 3 	imes 36 = 108$.

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

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