Students helping students, join us in improving Bored of Studies by donating and supporting future students!
Trebla said:Ok first of all: nCr = nCr+1 IS FALSE!!! Think about it, there's no way 6C1 = 6C2 for example. Similarly for n + 1Cr+1.
I think you meant: nCr + nCr + 1 = n + 1Cr + 1
LHS = nCr + nCr+1
= n! / [r!(n - r)!] + n! / {(r + 1)!(n - [r + 1])!}
= n! / [r!(n - r)!] + n! / {(r + 1)!(n - r - 1)!}
= n! / [r!(n - r - 1)!] { 1 / (n - r) + 1 / (r + 1) }
= n! / [r!(n - r - 1)!] x {r + 1 + n - r} / (n - r)(r + 1)
= n! / [r!(n - r - 1)!] x {n + 1} / (n - r)(r + 1)
= (n + 1)! / [(r + 1)!(n - r)!]
= (n + 1)! / [(r + 1)!(n + 1 - 1 - r)!]
= (n + 1)! / [(r + 1)!(n + 1 - {r + 1})!]
= n + 1Cr + 1
= RHS
4 x 3! = 4!micuzzo said:umm i forgot about this post lol... one question... i dont understand the third line and also, how/ why does (n-r-1)! x (n-r) = (n-r)1 <--- ive never really understood that.
hmmm... i think you may be onto somthing here... lollyounamu said:4 x 3! = 4!
yes?
Then y x (y-1)! = y! ?
then (n-r) x (n-r-1)! = (n-r)!
okay, i guess this explanation would be slightly better:micuzzo said:that was fast![]()
hmmm... i think you may be onto somthing here... lol
thanks.....
as if i didnt think of that *whispers to self*