Five different books are to be distributed among four students randomly. The probability that each child get…
Five different books are to be distributed among four students randomly. The probability that each child get atleast one book is
$\frac{21}{64}$
$\frac{15}{64}$
$\frac{31}{64}$
$\frac{51}{64}$
Solution
Total number of ways to distribute five different books among four students randomly is $4^5=2^{10}=1024$ and number of ways to distribute five different book among four students such that each child get atleast one book is
$
\frac{5 !}{1 ! 1 ! 1 ! 2 ! 3 !} \times 4 !=240
$
So, required probability is $\frac{240}{1024}=\frac{2^4 \times 3 \times 5}{2^{10}}=\frac{15}{64}$ Hence, option (2) is correct