Factorials A Quick and Easy Guide RAFS Education

Definition A facortial is the product of all positive numbers from n down. Written as: n!

Examples 10! = 10*9*8*7*6*5*4*3*2*1 5! = 5*4*3*2*1 1! = 1*1 0! = 1

10! = 10*9*8*7*6*5*4*3*2*1

5! = 5*4*3*2*1

1! = 1*1

0! = 1

Examples 3!+3! ≠ 6! Why? 3! = 3*2*1 = 6 3!+3! = 12 6! = 6*5*4*3*2*1 = 720 12 ≠ 720

3!+3! ≠ 6!

Why?

3! = 3*2*1 = 6

3!+3! = 12

6! = 6*5*4*3*2*1 = 720

12 ≠ 720

Examples Take the following: The answer is: (19*18*17*16*15*14*13*12*11) This is because when dividing factorials, the rules for cancelling out that apply to fractions also apply to factorials.

Take the following:

The answer is: (19*18*17*16*15*14*13*12*11)

This is because when dividing factorials, the rules for cancelling out that apply to fractions also apply to factorials.

Practice Example 1) Solve: 4! Example 2) Solve: 2!+3! Example 3) Solve: 5!/2! Example 4) Solve: 6!-4! (Are the following true?) Example 5) 4!+4! = 8! Example 6) 7!*6! = 10! Example 7) 5! = 5*4!

Example 1) Solve: 4!

Example 2) Solve: 2!+3!

Example 3) Solve: 5!/2!

Example 4) Solve: 6!-4!

(Are the following true?)

Example 5) 4!+4! = 8!

Example 6) 7!*6! = 10!

Example 7) 5! = 5*4!

Answers and Explanations Ex1) 4! = 4*3*2*1 = 24 Ex2) 2!+3! = (2*1)+(3*2*1) = 2+6 = 8 Ex3) 5!/2! = = 5*4*3 = 60 Ex4) 6!-4! = (6*5*4*3*2*1)-(4*3*2*1) = 720-24 = 696 Ex5) No. 4!+4! ≠ 8! Because 48 ≠ 40,320

Ex1) 4! = 4*3*2*1 = 24

Ex2) 2!+3! = (2*1)+(3*2*1) = 2+6 = 8

Ex3) 5!/2! = = 5*4*3 = 60

Ex4) 6!-4! = (6*5*4*3*2*1)-(4*3*2*1) = 720-24 = 696

Ex5) No. 4!+4! ≠ 8! Because 48 ≠ 40,320

Answers and Explanations Cont'd Ex6) Yes. 7!*6! = 10! Because 720*5040 = 3628800 Ex7) Yes. 5! = 5*4! Because 5*(4*3*2*1) = 120 and 5! = 120

Ex6) Yes. 7!*6! = 10! Because 720*5040 = 3628800

Ex7) Yes. 5! = 5*4! Because

5*(4*3*2*1) = 120 and 5! = 120

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