## Eyad 2 years ago ~I Need Someone Who Understand Permutations And Combinations *Very well* ..~

1. CliffSedge

For what? I don't know if I qualify as *very well* but I know how they work. You got something really complicated?

@CliffSedge :They are not very Complicated but i want someone to help me through some questions ....

3. CliffSedge

I'll at least take a look at one. I need to go in few minutes, though, but hopefully I can at least point you in the right direction.

hmmm. As a start : IF : $\Large C^{n}_{8} \times C^{n}_{6} \ge C^{n}_{7} \times C^{n}_{5}$ Prove That : $\Large n \ge13$ _

5. CliffSedge

Ok, so you know the combinations formula? $nCk=\frac{n!}{k!(n-k)!}$

yea

7. CliffSedge

Ok, and as a start, n≥k so it has to be at least 8, just given the values of k.

8. CliffSedge

It might also help to look at a simpler case using slightly smaller numbers to see how the factorials simplify. e.g. Show that 6C5 X 6C3 ≥ 6C4 X 6C2. That may give you some further insight.

9. CliffSedge

Sorry, should have said "e.g. Show if ... ≥ ..." Because it might not.

:D

To be honest thats not giving me at least a small hint .. I was looking for a short way to end this question .. Anyway Ty for your help :)

12. CliffSedge

If you play around with it a little bit, you'll see that the difference between n and k is important for the ultimate size of nCk - maybe also think of Pascal's Triangle . . .

13. CliffSedge

Yeah, sorry, I'm feeling rushed, 'cause I need to go take care of some other matters, so the shortcut isn't coming to me at the moment. Good luck!