If 7 different balls are distributed among 4 | vedclass

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(B) The total number of ways to distribute $7$ different balls into $4$ different boxes is $4^7$. To find the number of ways such that the first box c

Vedclass · Accepted Answer

$\frac{35}{64}\left(\frac{3}{4}\right)^4$

Vedclass · Answer

(B) The total number of ways to distribute $7$ different balls into $4$ different boxes is $4^7$. To find the number of ways such that the first box contains exactly $3$ balls,we first choose $3$ balls out of $7$ in ${}^7C_3$ ways. The remaining $4$ balls can be distributed among the other $3$ boxes in $3^4$ ways. Thus,the number of favorable ways is ${}^7C_3 	imes 3^4$. The required probability is $\frac{{}^7C_3 	imes 3^4}{4^7} = \frac{35 	imes 3^4}{4^7} = \frac{35}{4^3} 	imes \left(\frac{3}{4}ight)^4 = \frac{35}{64} \left(\frac{3}{4}ight)^4$.

If $7$ different balls are distributed among $4$ different boxes,then the probability that the first box contains $3$ balls is

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