Permutation and Combination

DEFINITION OF PERMUTATION :

A set of objects in which position / order is important

EXAMPLES :

1.   Our "order of 3 out of 16 pool balls example" is:

16!	=	16!	=	20,922,789,888,000	= 3,360
(16-3)!		13!		6,227,020,800

(which is just the same as: 16 × 15 × 14 = 3,360)

2.   How many ways can first and second place be awarded to 10 people?

10!	=	10!	=	3,628,800	= 90
(10-2)!		8!		40,320

(which is just the same as: 10 × 9 = 90)

FORMULA FOR PERMUTATION :

N!

(N-n)!

*! = FACTORIAL

*N = NUMBER SELECTED

DEFINITION OF COMBINATIONS :

A set of objects in which position / order is not important

                               

EXAMPLES :

1.   So, our pool ball example (now without order) is:

16!	=	16!	=	20,922,789,888,000	= 560
3!(16-3)!		3!×13!		6×6,227,020,800

         Or we could do it this way:

16×15×14	=	3360	= 560
3×2×1		6

FORMULA FOR COMBINATION :

N!

n!(N-n)!

*! = FACTORIAL

*N = NUMBER SELECTED