Question

when do you use \(\frac{n!}{r! (n-r)!}\) and \(\frac{n!}{(n-r)!}\)

Answer 1

aren't they the definitions of permutation and combination/

Answer 2

Hmm, that means you are confused about when to use permutations and when to use combinations - right?

Answer 3

Well, okay, let me use an example to illustrate.

Suppose I have a deck of cards before myself, and I am asked to pick any 5 cards, there are certain no. of ways to do it - that is you can pick a no. of 'combinations' - right?
So here, we gonna use 52C5 = 'C' for 'combine'.

Now, suppose I am now asked to 'pick' any 5 cards and then *arrange* them on the desk - so I have two tasks - first, picking up 5 cards and next, arrange it in a certain sequence, of which there are a certain no. of ways. This 'arrangement' basically means 'permutation' - which leads to the terminology "nPr"; 52P5 in our case.

Hope this cleared the cloud a bit.

Answer 4

can you not use those acronyms/abbreviations...please use the n!/(n-r)! thingies because i do not know your fancy notations @apoorvk i just learned this from viewing answers here =_=

Answer 5

Permutations are used to determine the number of ways to arrange something(order matters)
Combinations are used when it doesn't matter at all. We just wanna determine the number of combos we can form with some items(order doesn't matter here)

Answer 6

what about those replacement thingies?

Answer 7

and which is the permutation in my formulae

Answer 8

Replacement thingies?

Answer 9

dont know it huh?

Answer 10

i dont know...im just learning here =_=

Answer 11

i see thanks....im still pondering where they're used though

Answer 12

\[^nC_r=\frac{n!}{r! (n-r)!}\qquad^nP_r=\frac{n!}{(n-r)!}\]

Answer 13

uhmm yeah where are they used? i always do wrong in using them

Answer 14

Now that you know what nPr and nCr mean, scroll up and read it all. ^_^