# FACTORIAL WORKSHEET

Problems 1-5 : Find the value of.

Problem 1 :

8!

Problem 2 :

Problem 3 :

Problem 4 :

Problem 5 :

Problem 6 :

Evaluate the above expression, when n = 7 and r = 5.

Problem 7 :

Simplify the above expression for any n with r = 3.

Problem 8 :

Solve for n :

Problem 9 :

Solve for n :

n! + (n - 1)! = 30

Problem 10 :

What is the unit digit of the sum 2! + 3! + 4! + ........ + 22!?

8! = 8   6 ⋅  4 ⋅

= 40320

= 10  9  8

= 720

= 4

= 9  7

= 504

= 7 ⋅ 6 ⋅ 5 ⋅ 4 ⋅ 3

= 2520

n! = 5!

n = 5

n! + (n - 1)! = 30

n(n - 1)! + (n - 1)! = 30

(n - 1)!(n + 1) = 30

(n + 1)(n - 1)! = 5 ⋅ 6

(n + 1)(n - 1)! = 5 ⋅ (3 ⋅ 2 ⋅ 1)

(n + 1)(n - 1)! = 5 ⋅ 3!

Equate (n + 1) to 5.

n + 1 = 5

n = 4

2! = 2  1 = 2

3! = 3  1 = 6

4! = 4  1 = 24

5! = 5  4! = 5  24 = 120

6! = 6  5! = 6  120 = 720

7! = 7  6! = 7 × 720 = 5040

8! = 8  7! = 8  5040 = 40320

From 5! onwards for all n!, the unit digit is zero and hence the contribution to the unit digit is through (2! + 3! + 4!) only.

That is,

2! + 3! + 4! = 2 + 6 + 24

= 32

Therefore the required unit digit is 2.

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