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 ū 3 ū 2 ū 1 =  24 10! = 10  ū 9  ū 8  ū 7  ū 6   ū 5  ū  4  ū 3  ū 2  ū 1 = 3,628,800 3! = 3 ū 2  ū 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) Ę Ę Ę1  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 different 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 =