As there are 10 sportsmen out of which 5 are to be selected.

5 sportsmen can be selected out of 10 in ¹⁰C₅ ways.

Applying ⁿC_r =

We get,

⇒ ¹⁰C₅ =

252 ways

Hence, there are 252 ways of selecting 5 sportsmen from 10 sportsmen.