Question

In how many ways can $4$ prizes each having $1st,2nd$ and $3rd$ positions be given to three boys, if each boy is eligible to receive one prize for each event?

• A. ${}^{12}{P}_3$
• B. $6^4$
• C. $4^3$
• D. $4^6$

Answer 1

The correct option is B $6^4$

For each prize there are $3$ positions and each position obviously has to go to a different person.

So $3$ things are to be arranged at $3$ positions which is $3!=6$

Now there are $4$ prizes, hence total number of ways $=6^4$

Therefore the correct answer is $6^4$.