## Wolfboy 3 years ago Aysha has 8 pictures to hang over her couch. She wants to hang only 3 of them. Find how many ways she can choose the 3 pictures from the 8

1. A.Avinash_Goutham

8p3

2. CliffSedge

8c3 if order doesn't matter.

3. CliffSedge

Are you familiar with Pascal's Triange?

4. Wolfboy

uh not realy

5. A.Avinash_Goutham

u kno wat 8p3 is?

6. Wolfboy

not exactly

7. CliffSedge

I'm pretty sure this is a combination and not a permutation.

8. A.Avinash_Goutham

yup that's a combination nd it's 8c3

9. CliffSedge

Can use either Pascal's Triangle or the formula with factorials. For n=8, probably better off using the formula.

10. CliffSedge

nCx = n!/(x!(n-x)!) I think that's it. I'm just pulling it from memory, so I might have it mixed up with the other one, but it looks right.

11. Wolfboy

ok so how do we use this to make our equation. And sorry for the slowness i went surfing yesterday and i am still really tiered.

12. CliffSedge

A quick drawing of Pascal's Triangle shows it's 56, and 8!(3!(8-3)!) = the same.

13. CliffSedge

Do you know how to write out a factorial?

14. Wolfboy

uh i probably do but dont remember can you show me again?

15. CliffSedge

While I do that, do an internet search for "Pascal's Triangle." - It's useful not only for combinations, but also for finding the coefficients of an expanded power of a binomial.

16. CliffSedge

n! = n*(n-1)*(n-2)*...*1 e.g. 8! = 8*7*6*5*4*3*2*1 dividing factorials is easy because so many common factors cancel out. e.g. 8!/3! = 8*7*6*5*4

17. Wolfboy

Thanks for all of your help @CliffSedge