## 4 Solved Factorial Problems To Prepare For Bank of Baroda PO Exam

Dear Reader,

Below are four problems on basic calculations of factorials.

Note:

1) (n+1)! = (n+1)n!

2) (n+5)! = n!(n+1)(n+2)(n+3)(n+4)(n+5)

**Question 1**

Evaluate 29!/27!

a) 784 b) 812 c) 996 c) 128

**Answer :** b)812

Solution :

Given 29!/27!

By using the note (2), we can rewrite

29! = 27!(28)(29)

Then, 29!/27! = 27!(28)(29) / 27!

= 28 x 29

= 812

Hence the answer is 812.

**Question 2**

Evaluate (15! - 14!)/ 13!

a) 144 b) 169 c) 196 c) 125

**Answer :** c)196

Solution :

Given that, (15! - 14!)/ 13!

(15)14! - 14! / 13!

14!(15 - 1)/13!

14!(14)/13!

13!(14)(14)/13!

14 x 14

196

Hence the required answer is 196.

**Question 3**

Evaluate 13!/9!6!

a) 143/6 b) 155 c) 155/3 d) 187/7

**Answer :** a)143/6

Solution :

13! = 9! x 10 x 11 x 12 x 13

Then the given expression 13!/9!6! = 9! x 10 x 11 x 12 x 13 / 9!6!

13!/9!6! = 9! x 10 x 11 x 12 x 13 / 9!6!

= 10 x 11 x 12 x 13 / 6!

= 10 x 11 x 12 x 13 / 1 x 2 x 3 x 4 x 5 x 6

= 11 x 12 x 13 / 3 x 4 x 6

= 11 x 13 / 6

= 143/6

**Question 4**

Evaluate 1/12! + 1/13! - 1/14!

a) 522/16! b) 224/13! c) 195/14! d) 185/11!

**Answer :** c)195/14!

Solution :

Given that, 1/12! + 1/13! - 1/14!

1/12! = 14 x 13 / 14 x 13 x 12! = 14 x 13 / 14!

1/13! = 14 / 14 x 13! = 14/14!

1/14! = 1/14!

Then given expression = 14 x 13/14! + 14/14! - 1/14!

= (182 + 14 - 1)/14!

= 195/14!

Hence the answer is option c.