SIMPLIFYING THE FACTORIALS EXPRESSION WORKSHEET

Simplify the following expressions.     

Problem 1 :

(n + 2)! / n!

Solution

Problem 2 :

n / n!

Solution

Problem 3 :

(n - 1)! ∙ n! / (n!)²

Solution

Problem 4 :

(n + 5)! / (n + 1)!

Solution

Problem 5 :

((n + 1)!)³ / (n!)³

Solution

Problem 6 :

(n² - 1)! / (n²)!

Solution

Problem 7 :

(2n)! / (2n - 2)! ∙ 2!

Solution

Problem 8 :

(n - 1)! (n² + n)

Solution

Problem 9 :

(n + 5) (n + 4) (n + 3)!

Solution

Problem 10 :

n! (n² + 3n + 2)

Solution

Simplify without using a calculator.

Problem 1 :

6! / 5!

Solution

Problem 2 :

6! / 4!

Solution

Problem 3 :

6! / 7!

Solution

Problem 4 :

4! / 6!

Solution

Problem 5 :

100! / 99!

Solution

Problem 6 :

7! / (5! × 2!)

Solution

Simplify:

Problem 7 :

n! / (n - 1)!

Solution

Problem 8 :

(n + 2)! / n!

Solution

Problem 9 :

(n + 1)! / (n - 1)!

Solution

Simplify the following expressions.

Problem 10 :

5! / 6!

Solution

Problem 11 :

7! / 5!

Solution

Problem 12 :

(3!)² / 9

Solution

Problem 13 :

(3! ∙ 4!) / 5!

Solution

Problem 14 :

9! /(5! ∙ 3!)

Solution

Problem 15 :

(4 - 1)! / 4!

Solution

Problem 16 :

(2 ∙ 3)! / 3!

Solution

Problem 17 :

88! / 90!

Solution

Problem 18 :

(77! ∙ 2!)/ 78!

Solution

Problem 19 :

38! ∙ 3! / 39!

Solution

Express in factorial form:

Problem 1 :

7 × 6 × 5

Solution

Problem 2 :

10 × 9

Solution

Problem 3 :

11 × 10 × 9 × 8 × 7

Solution

Problem 4 :

(13 × 12 × 11) / (3 × 2 × 1)

Solution

Problem 5 :

1 / (6 × 5 × 4)

Solution

Problem 6 :

(4 × 3 × 2 × 1) / (20 × 19 × 18 × 17)

Solution

Problem 7 :

1 ∙ 2 ∙ 3 ∙ 4 ∙ 5 ∙ 6 ∙ 7 ∙ 8

Solution

Problem 8 :

1 ∙ 2 ∙ 3……100

Solution

Problem 9 :

1 ∙ 2 ∙ 3 ∙ 4 …. (n - 2) ∙ (n - 1) ∙ n

Solution

Problem 10 :

1 ∙ 2 ∙ 3 ∙ …. 56 ∙ 57 ∙ 58

Solution

Problem 11 :

1 ∙ 2 ∙ 3 ∙ 4 ∙ 5 ∙ … (5n - 4) ∙ (5n - 3) ∙ (5n - 2) ∙ (5n - 1)

Solution