Factorials, Combinations and Permutations Calculators

Factorials, Combinations and Permutations Calculators



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



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.


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




Combinations

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



Try this calculator... for C(n,r)








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Factorials, Combinations and Permutations Calculators