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(B) The total number of ways to distribute $5$ different books among $4$ students is $4^5 = 1024$. To ensure each student gets at least one book,we mu

Vedclass · Accepted Answer

$\frac{15}{64}$

Vedclass · Answer

(B) The total number of ways to distribute $5$ different books among $4$ students is $4^5 = 1024$. To ensure each student gets at least one book,we must distribute the books such that one student gets $2$ books and the other three students get $1$ book each. The number of ways to choose which student gets $2$ books is $\binom{4}{1} = 4$. The number of ways to choose $2$ books out of $5$ is $\binom{5}{2} = 10$. The number of ways to distribute the remaining $3$ books to the remaining $3$ students is $3! = 6$. Total favorable ways = $4 	imes 10 	imes 6 = 240$. The required probability is $\frac{240}{1024} = \frac{15}{64}$. Thus,option $B$ is correct.

Five different books are to be distributed among four students randomly. The probability that each child gets at least one book is

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