There are two urns. Urn A contains 3 distinct | vedclass

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(D) Step $1$: Select $2$ balls from Urn $A$ containing $3$ distinct red balls. The number of ways is $^3C_2 = 3$.Step $2$: Select $2$ balls from Urn $

Vedclass · Accepted Answer

$108$

Vedclass · Answer

(D) Step $1$: Select $2$ balls from Urn $A$ containing $3$ distinct red balls. The number of ways is $^3C_2 = 3$.Step $2$: Select $2$ balls from Urn $B$ containing $9$ blue balls. The number of ways is $^9C_2 = \frac{9 	imes 8}{2} = 36$.Step $3$: Since the operations are independent,the total number of ways to select the balls is $3 	imes 36 = 108$.Step $4$: After selection,the $2$ balls from $A$ are placed into $B$,and the $2$ balls from $B$ are placed into $A$. This is a single way of performing the swap for each specific selection.Therefore,the total number of ways is $108$.

There are two urns. Urn $A$ contains $3$ distinct red balls,and Urn $B$ contains $9$ blue balls. If two balls are selected at random from each urn and swapped,in how many ways can this operation be performed?

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