Question

In how many ways can the letters of the word 'UNIVERSAL' be arranged? In how many of these will E, R, S always occur together?

• A. 32240
• B. 30240
• C. 30240
• D. 31240
• E. None of these

Answer 1

The correct option is B 30240

(i) The word 'UNIVERSAL' has 9 letters which are all different. These 9 letters can be arranged amongst themselves in 9! ways.
(ii) 3 letters E, R, S can be taken to form 1 block. Thus, 7 letters U, N, I, V, ERS, A, L can be arranged in 7! ways.
Also, 3 letters E, R, S can be arranged amongst themseleves in 3! ways.
$\therefore$ The total number of arrangements $=7!\times 3!=30240.$