Question

In how many ways can $4$ prizes be distributed among $3$ students if each student can get all the $4$ prizes.

• A. $4!$
• B. $3^4$
• C. $3^4-1$
• D. $3^3$

Answer 1

The correct option is

A

$4!$

Let there be $3$ students $S_1,S_2,S_3$ and $4$ prizes $P_1,P_2,P_3,P_4$.

$\Rightarrow$ $S1$ students is eligible to receive any of $4$ prize, so $4$ ways.

$\Rightarrow$ $S2$ student is eligible to receive rest $3$ prize available, so $3$ ways.

$\Rightarrow$ $S3$ student is eligible to receive rest $2$ prize so $2$ ways.

$\therefore$ Total ways $=4\times 3\times 2=24$ways$=4!$ ways.