Question

The number of ways in which first, second and third prize can be distributed among $5$ competitors is?(no person can get more than a prize).

• A. $10$
• B. $15$
• C. $60$
• D. $125$

Answer 1

The correct option is C $60$

$n=5,r=3$

Number of permutations${=}^n{P}_r{=}^5{P}_3=\frac{5!}{(5-3)!}=\frac{5\times 4\times 3\times 2\times 1}{2\times 1}=5\times 4\times 3=60$

Hence, number of ways ways, in which the three prizes can be awarded$=60$