## Permutation & Combination Solved Questions For IBPS, SBI and Other Bank Exams - Page 2

**Question 1**

Four cycles are to be arranged in a row, in how many ways can be done?

a) 24 b) 20 c) 36 d) 16

**Answer :** a)24

Solution :

There are 4 cycles then n = 4,

And are arranged among themselves (r=4) in 4p4 ways.

we know that, npr = n! / (n - r)!

4p4 = 4!/(4 - 4)!

= 4!/0!

= 4!

= 1 x 2 x 3 x 4

= 24

Hence the required number of ways is 24.

**Question 2**

There are 3 number of fruits and are given to 4 number of children such that each gets atmost one. In how many ways this can be done?

a) 12 b) 28 c) 24 d) 36

**Answer :** c)24

Solution :

Three number of fruits are given to 4 number of children where each gets atmost one in npr ways where n = 4 and r = 3

we know that, npr = n! / (n - r)!

Here, 4p3 = 4!/(4 - 3)!

= 4!/1!

= 4!

= 24

Hence the answer is 24ways.

**Question 3**

In how many ways can five children sit in a row of 5 chairs?

a) 120 b) 322 c) 162 d) 360

**Answer :** a)120

Solution :

Number of permutations of all 5 children taking 5 chairs at a time is 5p5.

5p5 = 5! / (5 - 5)!

= 5!/0!

= 5!/1

= 1 x 2 x 3 x 4 x 5

= 120

Hence the required number of ways is 120.

**Question 4**

Ten students are writing a test. In how many ways can three students among them can score first three places?

a) 120 b) 328 c) 916 d) 720

**Answer :** d)720

Solution :

Ten students are writing a test. The number of ways in which first three places can be won is 10p3 ways.

10p3 = 10!/(10 - 3)!

= 10!/7!

= 7! x 8 x 9 x 10 / 7!

= 8 x 9 x 10

= 720

Hence the required number of ways is 720.