Factorials, Combinations and Permutations Calculators
كامل موسى الناصري

Factorials مضروب

Combinations توافيق

Permutations تباديل

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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.

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Combinations

An alternate form for combinations	UNORDERED
	لاحظ C(7,4) = C(7,3)  = 35 لماذا ؟

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

Enter n =

Enter r =

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Permutations

An alternate form for permutations	ORDERED
	لاحظ P(7,4) = 840 لكن P(7,3) = 210

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

Enter n =

Enter r =