Question

In how many ways can $4$ distinguishable balls be distributed among $9$ distinguishable boxes if no box can contain more than one ball

• A. ${}^9{C}_4$
• B. ${}^9{P}_4$
• C. $9^4$
• D. $4^9$

Answer 1

The correct option is B ${}^9{P}_4$

$4$ balls distinguishable from $9$ balls

No boxes contain more than one ball

Since there is no repetition

$\Rightarrow$ only four boxes will be filled

$\Rightarrow$ Selecting four boxes and arranging ${}^9{P}_4$

$4$ balls be arranged in $4!$ ways

Number of ways

${=}^9{P}_4\times 4!{=}^9{P}_4$