Binomial Theorem urgent help! (1 Viewer)

[fahadmumtaz88]

Can someone plz do this one for me. thanks

It was a bit hard to write it on this so ive attached the question.

 

[Nobuo Uematsu]

10Ck\10C(k-1)
=10!\k!(10-k)! * (k-1)!(10-(k-1))!\10!
=(k-1)!(10-k+1)!\k!(10-k)!
=(10-k+1)\k
=(11-k)\k

 

[Trev]

{10!/[(10-k)!k!]}*{[(10-k+1)!(k-1)!]/10!} <- inverse and multiply of (10)C(k-1).
[(10-k+1)!(k-1)!]/[(10-k)!k!]
- (10-k+1)! [ie. (10-k+1)(10-k)(10-k-1)....!] cancels with (10-k)!
- (k-1)! [ie. (k-1)(k-2)...!] cancels with k! [ie. (k)(k-1)(k-2)...!]
Leaving:
(10-k+1)/(k)
= (11-k)/k as required.

 

[haboozin]

always use ur nCr factorials rules for a question like this - then it becomes easy!!!