Question

At a high school, 7 students volunteer for a committee. How many different 5-person committees can be chosen?

Answer 1

Solution:

Committee of 5 persons need to be made.

Out of 7 student volunteer there will be a selection of 5 students.

So, the number of ways in which 5 persons will get selected will be =>

$^{7}C_{5}$

$\frac{7!}{(7-5)! 5!}$

$\frac{7 * 6 * 5!}{2! 5!}$

$\frac{7 * 6 }{2 * 1}$

$7 * 3$

$21$

There are 21 ways in which we can have different 5-person committees which can be chosen.

Combination is a way by which we select terms from a collection given where the order of selection doesn't matter.

$^{n}C_{r} = \frac{n!}{(n-r)! r!}$

$^{n}C_{r} \ can \ also \ be \ written \ as \ _{n}C_{r} \ , \ C(n,r) \ , \ C_{n} ^{r}$

Answer 2

Answer:

21

Step-by-step explanation:I don’t