Question

The number of permutations that can be formed out of the letters of the word $"SERIES"$ taking three letters together is:

• A. $40$
• B. $42$
• C. $45$
• D. $48$

Answer 1

The correct option is B $42$

Given letters $S,S,E,E,R,I$
There are $4$ distinct letters $S,E,R,I$.
We ned to form $3$ - lettered words.
Case 1: All $3$ letters are distinct
Choosing $3$ letters $={}^4{C}_3$
Rearrangements $=3!$
Total $={}^4{C}_3\times 3!=24$
Case 2: $2$ are of one kind, $1$ is different
There are choices for repeated letters $(S,E)={}^2{C}_1$
We need to choose $1$ from remaining 3 letters $={}^3{C}_1$
These can be rearranged in $\frac{3!}{2!}$ ways.
Total $=2\times 3\times 3=18$
$\therefore$ Required $=24+18=42$ words.
Hence, the answer is $42$.