# How many different teams of 11 players can be chosen from 15 players?

Question:

How many different teams of 11 players can be chosen from 15 players?

Solution:

Condition: Each student has an equal chance of getting selected.

Imagine selecting the teammates one at a time. There are 15 ways of selecting the first teammate, 14 ways of selecting the second, 13 ways of selecting the third teammate, and so on down to 5 ways of selecting the eleventh teammate.

This is a problem of combination

$\Rightarrow \mathrm{n}=15 \& \mathrm{r}=11$

$\Rightarrow{ }^{n} C_{r}={ }^{15} C_{11}$

$\Rightarrow{ }^{15} C_{11}=\frac{15 !}{(15-11) ! \times 11 !}$

$\Rightarrow{ }^{15} C_{11}=\frac{15 !}{4 ! \times 11 !}$

$\Rightarrow{ }^{15} C_{11}=\frac{15 \times 14 \times 13 \times 12 \times 11 !}{4 ! \times 11 !}$

$\Rightarrow{ }^{15} \mathrm{C}_{11}=\frac{15 \times 14 \times 13 \times 12}{4 \times 3 \times 2 \times 1}$

$\Rightarrow{ }^{15} \mathrm{C}_{11}=1365$

Ans: There can be 1365 different ways of choosing 11 players from a squad of $15 .$

This means there can be 1365 eleven-member teams formed with 15 players.