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. $9!\text{and}30240$
• B. $9!\text{and}40240$
• C. $9!\text{and}20240$
• D. $9!\text{and}60240$

Answer 1

The correct option is A $9!\text{and}30240$

(i) The word UNIVERSAL has 9 letters which are all different. These 9 letters can be arranged amongst themselves in total of 9! ways.
(ii) Three letters E, R, S can be taken to form one 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 themselves in 3! ways.
$\therefore$ The number of arrangements
$=7!\times 3!$
$=30240$