Question

The number of words that can be made by rearranging the letters of the word APURBA so that vowels and consonants alternate is

• A. 18
• B. 35
• C. 36
• D. none of these

Answer 1

Answer: (C)

36

We divide the problem into $2$ cases

(1) Starting with a vowed and ending with a consonants.

(2) Starting with a consonants and ending with a vowel.

Case (1): The three vowels $A,A,U$ can be arranged in $3$ ways

$(A-A-U,A-U-A,U-A-A)$

Now the three consonants can be placed in $6$ different ways $3\times 6$ ways.

Case (2): as in the above case there will be $18$ ways in which this can be done

( just swap the places of the words generated above alternatly).

Therefore there are $18+18$ i.e., $36$ ways.