Question

Consider the word ${}^{\prime }RAMAYAN{A}^{\prime }$, then the total number of possible words

• A. When all $A^{\prime }s$ are together is $120$
• B. When no two $A^{\prime }s$ are together is $120$
• C. When it starts with $A$ and ends with $A$ is $360$
• D. When it starts with any consonant is $210$

Answer 1

Answer: (A), (B), (C)

The correct options are
A When all $A^{\prime }s$ are together is $120$
B When no two $A^{\prime }s$ are together is $120$
C When it starts with $A$ and ends with $A$ is $360$

${}^{\prime }RAMAYAN{A}^{\prime }$
It has ${}^{\prime }R,M,Y,N$ and $4A^{\prime }s$
When all $A^{\prime }s$ are together, total words will be $\frac{5!}{4!}\times 4!=120$

Total words when no two $A^{\prime }s$ are together
Arrange the letters ${}^{\prime }R,M,Y,N$ 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 $=5\times 4!=120$

When the word starts with $A$ and ends with $A$
Total ways $\frac{6!}{2!}=360$


When word starts with any consonant is, i.e. by ${}^{\prime }R,M,Y,N$
$=4\times \frac{7!}{4!}=840$