Question

The high school dance team is holding auditions to fill the spots of four members that graduated. If 10 people try out for the 4 positions, and order does not matter, how many possible combinations exist?

Answer 1

I created a little chart for these at one point, but lost it

Answer 2

aww

Answer 3

Let me see if I can find it again

Answer 4

Here's the website I used to create the charts. I must have been a genius back then because I don't even remember it anymore

Answer 5

http://www.mathsisfun.com/combinatorics/combinations-permutations.html

Answer 6

It's like you consider four things:

Combination
Permutation
Order
Repetition

Answer 7

Order doesn't matter..... could it be 10C4 ?\[\left(\begin{matrix}10 \\ 4\end{matrix}\right)=\frac{10!}{4!6!}=\frac{10*9*8*7*6!}{4*3*2*6!}=210\]

Answer 8

And based on that, there is a formula

Answer 9

i was just about to do that formula :)

Answer 10

We know it is combinations and we know order doesn't matter, so there is a formula that corresponds with that

Answer 11

But there's like several formulas for different scenarios

Answer 12

I'd have to put them all together again.

Answer 13

Did you find all four of them?

Answer 14

If not, I can post them again

Answer 15

Animalani actually got the answer i just had to find 1

Answer 16

and it corresponded with the 4 answers that were given thanks for your help though

Answer 17

@AnimalAin just like posting answers.

Answer 18

Giving answers never really helps anyone understand anything though

Answer 19

I thought I showed the justification and work for it, as well....

Answer 20

You did, but you explained nothing.

Answer 21

Hero i found the formula out while animalain was typing so either way we would have came to the same conclusion

Answer 22

so it somewhat helped me i guess

Answer 23

@jazzy2346 , I'm trying to give @AnimalAin a hard time either way.

Answer 24

lol