Question

Ten students are participating in a race. The number of ways the first three places can be won is:

• A. $3$
• B. ${}^{10}{C}_3$
• C. ${}^{10}{P}_3$`
• D. ${}^{10}{P}_4$

Answer 1

Answer: (C)

${}^{10}{P}_3$`

Number of ways of selecting winners for top three places from $10$ students is ${}^{10}{C}_3$
but the first three positions can also be arranged in $3!$.
Hence required number of ways is ${=}^{10}{C}_3\times 3!{=}^{10}{P}_3$