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

Answer 1

Ans-7!(no. of ways to arrange the letters assuming ERS as 1 letter)*3!(no. of ways to arrange E,R,S in ERS)

Answer 2

Solution:

• The letters of the word UNIVERSAL can be arranged in 9! ways.

• The number of ways in which E,R,S always occur together should be 7! 3!

Explanation:

The given word 'UNIVERSAL' has 9 different letters.

We know that n different things can be arranged in n! ways.

Hence, 9 different things can be arranged in 9! ways.

Thus, the letters of the word UNIVERSAL can be arranged in 9! ways.

Now, we use the concept that whatever comes together can be considered as a single unit in order to find the second part of the question.

{ERS} can be considered as a single unit. Hence, we have {ERS},{U},{N},{I},{V},{A},{L} which are 7 units. These can be arranged in 7! ways.

{ERS} can be arranged themselves in 3! ways.

Hence, total number of ways in which E,R,S always occur together should be  7! 3!