Question

Seven athletes are participating in a race. If there are three prizes $Gold,Silver$ and $Bronze$, then the number of ways in which the prizes can be distributed to the athletes is

• A. $35$
• B. $105$
• C. $210$
• D. $420$

Answer 1

The correct option is C $210$

Out of the $7$ atheletes only $3$ athletes will win prizes.

Therefore, the number of permutations of $7$ objects taken $3$ at a time is :

${}^7{P}_3=\frac{7!}{4!}=7\times 6\times 5=210$

Hence, there are $210$ ways that the three athletes win the prizes.