There are three bags B_1,B_2,and B_3 containi | vedclass

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(C) Let $R_i$ and $W_i$ denote drawing a Red or White ball from bag $i$ respectively.Case $1$: Red ball transferred from $B_1$ to $B_2$,then Red ball

Vedclass · Accepted Answer

$180$

Vedclass · Answer

(C) Let $R_i$ and $W_i$ denote drawing a Red or White ball from bag $i$ respectively.Case $1$: Red ball transferred from $B_1$ to $B_2$,then Red ball transferred from $B_2$ to $B_3$.Number of ways = (Ways to pick Red from $B_1$) $	imes$ (Ways to pick Red from $B_2$ after receiving Red from $B_1$) $	imes$ (Ways to pick any ball from $B_3$ after receiving Red from $B_2$).Ways = $^2C_1 	imes ^6C_1 	imes ^6C_1 = 2 	imes 6 	imes 6 = 72$.Case $2$: White ball transferred from $B_1$ to $B_2$,then White ball transferred from $B_2$ to $B_3$.Number of ways = (Ways to pick White from $B_1$) $	imes$ (Ways to pick White from $B_2$ after receiving White from $B_1$) $	imes$ (Ways to pick any ball from $B_3$ after receiving White from $B_2$).Ways = $^3C_1 	imes ^6C_1 	imes ^6C_1 = 3 	imes 6 	imes 6 = 108$.Total ways = $72 + 108 = 180$.

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