Question

In how many ways can a foot ball team of 11 players be selected from 15 players, if a particular player always be included?

• A. 1001
• B. 1002
• C. 1003
• D. 1004

Answer 1

Answer: (A)

1001

Here, we want to find the number of ways of selecting 11 players out of 15.
$\Rightarrow$ The required no. of ways
$=C(15,11)=\frac{15!}{11!4!}=\frac{15\times 14\times 13\times 12}{4\times 3\times 2\times 1}$
$15\times 7\times 13=1365$
A particular player to be included So, we have to select 10 players out of 14.
$\Rightarrow$ The required no. of ways
$C(14,10)=\frac{14!}{10!4!}=\frac{\mathrm{14.13.12.11}}{\mathrm{4.3.2.1}}$
$=\mathrm{7.13.11}=1001$