## mynameisjanelle 3 years ago In how many ways can a gymnastics team of 4 be chosen from 9 gymnasts?

1. mynameisjanelle

dont get this one, could someone show me the steps?

2. lgbasallote

"chosen" so you use combinations

3. apple_pi

from 9 choose 4. 9C4 = ...

4. lgbasallote

arent you missing something?

5. mynameisjanelle

362880?

6. lgbasallote

that's 9!

7. apple_pi

don't forget to divide by all the same combinations (n-r)!

8. lgbasallote

$9C4 \implies \frac{9!}{4!(9-4)!}$

9. apple_pi

dividing by (n-r)! is what separates the combination formula from the permutation, because you are not counting all the different arrangements

10. lgbasallote

isnt dividing r! what separates it?

11. lgbasallote

$nCr = \frac{n!}{r!(n-r)!}$ $nPr = \frac{n!}{(n-r)!}$

12. lgbasallote

dividing by r! is just the difference i see =))

13. mynameisjanelle

126!!

14. lgbasallote

i hope those ! arent factorials :p haha

15. lgbasallote

anyway yeah. 9C4 = 126

16. mynameisjanelle

ya:P

17. apple_pi

Ooops, I meant r! not (n-r)! for all the above posts. Sorry :o