Question

Suppose four balls labelled $1,2,3,4$ are randomly placed in boxes $B_1,B_2,B_3,B_4$. The probability that exactly one box is empty is

• A. $\frac{8}{256}$
• B. $\frac{9}{16}$
• C. $\frac{27}{256}$
• D. $\frac{9}{64}$

Answer 1

Answer: (B)

$\frac{9}{16}$

Total number of ways in which $4$ different balls can be placed in $4$ distinct boxes$=4^4$

number of ways in which exactly $1$ box is empty${=}^4{C}_1\times \frac{4!}{2!}\times 3$

$\therefore$ The probability that exactly one box is empty is$=\frac{4\times 4\times 3\times 3}{4^4}=\frac{9}{16}$