Question

Find the number of permutations which can be formed out of the letters of the word series taken three together?

• A. $32$
• B. $36$
• C. $42$
• D. $46$

Answer 1

The correct option is C $42$

There are $4$ different distinct letters $s,e,r,i$ with s $\xi$ e repeating.

The $3$ letters can be of the order abc or aab.

$\Rightarrow$ For $abc$ :

From $4$ letters we need to choose $3={}^4{C}_3\xi$ these can be arranged in $3!$ ways.

$\therefore 4\times 6=24$ ways

$\Rightarrow$ For $aab$ :

From $2$ repeating letters we choose $1\xi$ fro, remaining $3$ letters we choose $1$

$\therefore {}^2{C}_1\times {}^3{C}_1=6$

These letters can be arranged in $\frac{3!}{2!}$ ways.

$\therefore 6\times 3=18$ ways

Total $=24+18=42$ ways

Hence, the answer is $42.$