# From a class of 25 students, 4 are to be chosen for a competition.

Question:

From a class of 25 students, 4 are to be chosen for a competition. In how many ways can this be done?

Solution:

This is a case of combination:

Here

$\mathrm{n}=25$

$r=4$

$\Rightarrow{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}={ }^{25} \mathrm{C}_{4}$

$\Rightarrow{ }^{25} \mathrm{C}_{4}=\frac{25 !}{(25-4) ! \times 4 !}$

$\Rightarrow{ }^{25} \mathrm{C}_{4}=\frac{25 !}{21 ! \times 4 !}$

$\Rightarrow{ }^{25} \mathrm{C}_{4}=\frac{25 \times 24 \times 23 \times 22 \times 21 !}{21 ! \times 4 !}$

$\Rightarrow{ }^{25} \mathrm{C}_{4}=\frac{25 \times 24 \times 23 \times 22}{4 \times 3 \times 2 \times 1}$

$\Rightarrow{ }^{25} \mathrm{C}_{4}=12650$ possible ways.

Ans: In 12650 ways, from a class of 25 students, 4 can be chosen for a competition.