Question

There are 6 students. 2 of them are chosen for the position of president and Vice President. How many ways do we have to choose the students from the 6 students?

Answer 1

We have 15 ways to chose 2 students for the position of president and Vice President

Solution:

Given that,

There are 6 students. 2 of them are chosen for the position of president and Vice President.

To find: number of ways we have to choose the students from the 6 students

So now we have 6 students, out of which we have to choose 2 students

As we just have to select the students. We can use combinations here.

In combinations, to pick "r" items from "n" items, there will be $^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}$ ways

$^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}=\frac{n !}{(n-r) ! r !}$

Then, here we have to pick 2 out of 6:

Total students = n = 6

students to be selected = r = 2

$\begin{aligned} 6 C_{2} &=\frac{6 !}{(6-2) ! 2 !} \\\\ 6 C_{2} &=\frac{6 !}{4 ! 2 !} \\\\ 6 C_{2} &=\frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{4 \times 3 \times 2 \times 1 \times 2 \times 1} \\\\ 6 C_{2} &=15 \end{aligned}$

Thus we have 15 ways to chose 2 students for the position of president and Vice President