Question

The letters of word "RADHIKA" are permuted are arranged in alphabetical order as in English dicitionary. The number of words the appear before the word "RADHIKA" is:

• A. 2193
• B. 2195
• C. 2119
• D. 2192

Answer 1

The correct option is A 2193

The given word is 'RADHIKA'

total no. of alphabets $=7$ (which includes $2A^{\prime }s$)

No. of words starting with A

$A....................$

$=6!=720$

No. of words starting with $D=\frac{6!}{2!}=\frac{720}{2}=360$

No. of words starting with $H=\frac{6!}{2!}=360$

No. of words starting with $I=\frac{6!}{2!}=360$

No. of words starting with $K=\frac{6!}{2!}=360$

So, total no. of words starting from $A,B,H,I,K$ is $720+360+360+360=2160$

words starting from $R$

having $A$ on second position

i) on third position $RAA........$

$=4!=24$

Thus there are $2160+24=2184$ words before $RNA.............$comes

$\to$ Now A can also appear on fourth position

No. of such words $=3!=6$

$RADH.....$ when A comes on $5$ position

No. of such words $=2!=2$

$RADHA.....$ When $A$ ncomes on $6$ position =$1$ word

Then comes the word $RADHIKA$

No. of words appearing before $=2184+92193$ word.