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Question

Consider the word RAMAYANA, then the total number of possible words
  1. When all As are together is 120
  2. When no two As are together is 120
  3. When it starts with A and ends with A is 360
  4. When it starts with any consonant is 210


Solution

The correct options are
A When all As are together is 120
B When no two As are together is 120
C When it starts with A and ends with A is 360
RAMAYANA
It has R,M,Y,N and 4As
When all As are together, total words will be 5!4!×4!=120

Total words when no two As are together
Arrange the letters R,M,Y,N in alternate manner, such that there will be 5 spaces left, so that can be filled by 5 ways

So the total number of words =5×4!=120

When the word starts with A and ends with A
Total ways 6!2!=360


When word starts with any consonant is, i.e. by R,M,Y,N
=4×7!4!=840
 

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