Question

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

• A. When it starts with $R$ and ends with $M$ is $30$
• B. When it starts with vowel is $840$
• 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)

When it starts with $A$ and ends with $A$ is $360$

${}^{\prime }RAMAYAN{A}^{\prime }$
It has ${}^{\prime }R,M,Y,N^{\prime }$ and $4A^{\prime }s$
$\left(i\right)$Number of words starting with $R$ and ending with $M$ is
$=\frac{6!}{4!}=30$

$\left(ii\right)$Number of words starts with vowel is, i.e. by ${}^{\prime }{A}^{\prime }$
$=\frac{7!}{3!}=840$

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


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