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 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 =