Factorials, Combinations and Permutations

Factorials, Combinations and Permutations









Factorials

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





Combinations

An alternate form for combinations UNORDERED


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









Permutations

An alternate form for permutations ORDERED


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











Factorials, Combinations and Permutations Calculators




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Factorials, Combinations and Permutations