permutations and combinations

k today im teaching you how to do permutations and combinations. it is a really easy process if you know what you are doing. you use permutation if the order is important and you use combination if the order is not important. for permutation you use the formula:   n! / (n-r)! or nPr. for combination you use the formula:       n! / (n-r)! r! or nCr. so i will provide an example below to show you exactly what all this means.


EX:
a) in how many ways can a club with 20 members choose a president, vice president, secratary
b) in how many ways can they choose a 4 person govering council
 

a)order does matter because it is three different ranks
so it is nPr
plug in numbers
20 P 3--- 3 because pres, vice pres and sec
20! / (20-3)!
= 20! / 17!
17! cancels and leaves you with 20*19*18 = 6840 ways

b)order does not matter because positions are all the same
so its is nCr
plug in
20 C 4
20! / (20-4)! 4!
20! / 16! 4!
16! cancels so you are left with 20*19*18*17 / 4*3*2*1 = 4845 ways