Question:
In how many ways can 5 sportsmen be selected from a group of 10?
Solution:
As there are 10 sportsmen out of which 5 are to be selected.
5 sportsmen can be selected out of 10 in ${ }^{10} \mathrm{C}_{5}$ ways.
Applying ${ }^{n} C_{r}=\frac{n !}{r !(n-r) !}$
We get,
$\Rightarrow{ }^{10} C_{5}=\frac{10 !}{5 !(10-5) !}$
$\Rightarrow 252$ ways
Hence, there are 252 ways of selecting 5 sportsmen from 10 sportsmen.