## Permutation and Combination

#### Permutation and Combination

1. In how many ways, the letters of the word 'ARMOUR' can be arranged ?

1. Number of arrangements n ! /( p ! q ! r ! )
Total letters = 6, but R has come twice.
So, required number of arrangements
= 6 ! / 2 !

##### Correct Option: E

Number of arrangements n ! /( p ! q ! r ! )
Total letters = 6, but R has come twice.
So, required number of arrangements
= 6 ! / 2 ! = (6 x 5 x 4 x 3 x 2 !) / 2 ! = 360

1. In how many ways, the letters of the word 'BANKING' can be arranged ?

1. Total letters = 7, but N has come twice.
So, required number of arrangements = 7 ! / 2 !

##### Correct Option: D

Total letters = 7, but N has come twice.
So, required number of arrangements = 7 ! / 2 !
= [7 x 6 x 5 x 4 x 3 x 2 ! ] / 2 ! = 2520

1. In how many ways, the letters of the word 'STRESS' can be arranged ?

1. Required number of arrangements = 6 ! / 3 ! [∵ S has come thrice ]

##### Correct Option: D

Required number of arrangements = 6 ! / 3 ! [∵ S has come thrice ]
= [ 6 x 5 x 4 x 3! ] /3 !
= 120

1. In how many different ways, the letters of word 'FINANCE' can be arranged ?

1. Total number of letters = 7, but N has come twice.
So, required number of arrangements = 7 ! / 2 !

##### Correct Option: E

Total number of letters = 7, but N has come twice.
So, required number of arrangements = 7 ! / 2 !
= [7 x 6 x 5 x 4 x 3 x 2! ] / 2!
= 2520

1. In how many different ways, can the letters of the word 'INHALE' be arranged ?

1. The word 'INHALE' has 6 distinct letters.
∴ Number of arrangements = n !

##### Correct Option: A

The word 'INHALE' has 6 distinct letters.
∴ Number of arrangements = n ! = 6 !
= 6 x 5 x 4 x 3 x 2 x 1
= 720