(i) RUSSIA

Here's are 6 letters in the word ‘RUSSIA’ out of which 2 are S’s and the rest all are distinct.

Therefore by using the formula,

n!/ (p! × q! × r!)

The total number of arrangements = 6! / (2!)

= [6 × 5 × 4 × 3 × 2 × 1] / 2!

= 6 × 5 × 4 × 3

= 360

(ii) SERIES

There are 6 letters in the word ‘SERIES’ out of which 2 are S’s, 2 are E’s and the rest all are distinct.

Therefore by using the formula,

n!/ (p! × q! × r!)

The total number of arrangements = 6! / (2! 2!)

= [6 × 5 × 4 × 3 × 2 × 1] / (2! 2!)

= 6 × 5 × 3 × 2 × 1

= 180

(iii) EXERCISES

There are 9 letters in the word ‘EXERCISES’ out of which 3 are E’s, 2 are S’s and the rest all are distinct.

Therefore by using the formula,

n!/ (p! × q! × r!)

The total number of arrangements = 9! / (3! 2!)

= [9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1] / (3! 2!)

= [9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1] / (3 × 2 × 1 × 2 × 1)

= 9 × 8 × 7 × 5 × 4 × 3 × 1

= 30240

(iv) CONSTANTINOPLE

Here's 14 letters in the word ‘CONSTANTINOPLE’ out of which 2 are O’s, 3 are N’s, 2 are T’s and the rest all are distinct.

Therefore by using the formula,

n!/ (p! × q! × r!)

The total number of arrangements = 14! / (2! 3! 2!)

= 14!/ (2 × 1 × 3 × 2 × 1 × 2 × 1)

= 14! / 24