Question

Combinations: A schools academic consists of 7 students but only 3 can participate. How many different 3 person teams can be formed from 7 students?

so

7!
---
(7-3)!3!
??

Answer 1

good, just evaluate that and you're done

Answer 2

I got 105 tho..
because 7x6x5x4x3x2
------------
4x3x2x3x2
I canceled out the 2,3,4,2

ehh im confused /:

Answer 3

it's not 105

Answer 4

you are forgetting about the 3! in the denominator

Answer 5

is it 35?

Answer 6

7!
---------
(7-3)!3!


7!
---------
4!3!



7*6*5*4!
---------
4!3!



7*6*5
---------
3!


7*6*5
---------
3*2*1


35


So you are correct, it's 35

Answer 7

Faster way to do it

There are 7 ways to fill slot 1
There are 6 ways to fill slot 2
There are 5 ways to fill slot 3

so there are 7*6*5 = 210 ways to do this if ordered mattered....but it does NOT matter

So you have to divide by 3! = 3*2*1 = 6 to get

210/6 = 35

Answer 8

This is why you'll see

n C r = (n P r)/( r! )

Answer 9

thank you!! :)

Answer 10

sure thing