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6.Permutation and Combination
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There are three bags $B_1$,$B_2$ and $B_3$ containing $2$ Red and $3$ White, $5$ Red and $5$ White, $3$ Red and $2$ White balls respectively. A ball is drawn from bag $B_1$ and placed in bag $B_2$, then a ball is drawn from bag $B_2$ and placed in bag $B_3$, then a ball is drawn from bag $B_3$. The number of ways in which this process can be completed, if same colour balls are used in first and second transfers (Assume all balls to be different) is
A
$108$
B
$150$
C
$180$
D
$200$
Solution
${\,^2}{{\rm{C}}_1} \times {\,^6}{{\rm{C}}_1} \times {\,^6}{{\rm{C}}_1} + {\,^3}{{\rm{C}}_1} \times {\,^6}{{\rm{C}}_1} \times {\,^6}{{\rm{C}}_1}$
$72+108=180$
Standard 11
Mathematics
