Question

How many ways are there to choose a committee of 5 people from a group of 15 people?

How do you solve this what is the equation?

Answer 1

15C5

Like, fifteen, choose five. ^_^

You know the formula for nCr?

Answer 2

no I dont

Answer 3

You know what "factorial" means?

Answer 4

yes

Answer 5

Okay, good. Then the formula for nCr is as follows:
\[\Large _nC_r = \frac{n!}{r!\cdot (n-r)!}\]
Just plug in :)

Answer 6

is n 5 and 4 15?

Answer 7

What do you think? ;)
in general, n should be the larger number.

Answer 8

Did you get your answer?

Answer 9

is 3,003

Answer 10

That's right ^^

Remember, that's what you do whenever you're asked how many ways you can pick r distinct members from a set of n.

nCr.

Good job :)

Answer 11

why can't you use nPr

Answer 12

Good question. nPr
\[\Large _nP_r = \frac{n!}{(n-r)!}\]
is used for when ORDER matters.

For instance, if the question were how many ways we can ARRANGE five members from a group of 15 people in a ROW, then the answer would involve nPr instead.

Answer 13

thanks