Question

In how many ways can $8$ distinguishable balls be distributed among $5$ distinguishable boxes if any box can contain more than one ball?

• A. $9^4$
• B. ${}^9{P}_4$
• C. ${}^9{C}_4$
• D. $5^8$

Answer 1

The correct option is D $5^8$

$8$ distinguishable balls

$5$ distinguishable boxes

each box can be placed in $5$ ways (therefore thry are in five boxes)

$\Rightarrow$ Then number of ways of arranging $8$ balls $(5{)}^8$

Therefore Number of ways $=(5{)}^8$