Factorials, Combinations and Permutations Calculators

Factorials, Combinations and Permutations Calculators
by Joe McDonald

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

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.

An alternate form for *combinations*	unordered

	Notice C(7,4) = C(7,3) = 35 Why?

An alternate form for *permutations*	ordered

	Notice P(7,4) = 840 but P(7,3) = 210