Combination and Permutation

Permutation means when the order is importance
The formula used is : nPr=n!/(n-r)!
When order isnt important you use combination  
The formula used is:Cr=n!/(n-r)!r!


Example:what order could 16 pool balls be in?After choosing, number "14" you can't choose it again.

Ex 2:Permutation: 16 × 15 × 14 × 13 × ... = 20,922,789,888,000

Combination:Picking a team of 3 people from a group of 10. 


C(10,3) = 10!/(7! * 3!) = 10 * 9 * 8 / (3 * 2 * 1) = 120.


Ex 3:Permutation: Picking a President, VP and Waterboy from a group of 10. 
P(10,3) = 10!/7! = 10 * 9 * 8 = 720.


Combination: Choosing 3 desserts from a menu of 10. 
C(10,3) = 120.


Permutation: Listing your 3 favorite desserts, in order, from a menu of 10.


 P(10,3) = 720.


Ex 4:Given 4 people, Bob, Mike, Sue and Alice, how many different ways can these three people be arranged where order matters?

Finding all possible arrangements of Bob, Mike, Sue and Alice where order matters would be:
BMSA,    BMAS,    BSMA,    BSAM,    BAMS,    BASM
MBSA,    MBAS,    MABS,    MASB,    MSBA,    MSAB
SBMA,    SBAM,    SMBA,    SMAB,    SABM,    SAMB
ABMS,    ABSM,    AMBS,    AMSB,    ASBM,    ASMB

There are 24 ways to arrange the four people four at a time,   or   4!