Factorials, Combinations and Permutations Calculators
by Joe McDonald

 Factorials Combinations Permutations

Factorials

A factorial is denoted using an ! symbol.  For example...

 Try this calculator... for n! Enter n =
 4! = 4 × 3 × 2 × 1 =  24 10! = 10  × 9  × 8  × 7  × 6   × 5  ×  4  × 3  × 2  × 1 = 3,628,800 3! = 3 × 2  × 1 =  6 As you can see,  10!, pronounced 10 factorial, is a large number.  What about 20! or 100!? Most calculators including the TI 's series will only calculate factorials up to 69! 69! = 1.711224524 E 98 = 107,112,245,240,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000 Other important facts.... n! = n(n - 1)(n -2) · · ·1  where n is an integer greater than 0 1! = 1 0! = 1 ( -2)! is undefined

Example

There are n! distinct arrangement of  n distinct objects.  If 3 people race, there are 3! = 6 different outcomes.   If you want to arrange 6 different books on a shelf, there are 6!   = 720 diiferent arrangements.

Combinations

 An alternate form for combinations unordered  Notice  C(7,4) = C(7,3)  = 35 Why?
 Try this calculator... for C(n,r) Enter n = Enter r =

Permutations

 An alternate form for permutations ordered  Notice P(7,4) = 840 but P(7,3) = 210
 Try this calculator... for P(n,r) Enter n = Enter r =