Question

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

Answer 1

Given letters $S,S,E,E,R,I$

There are $4$ district letters $S,E,R,I.$

We need to form $3-$lettered words.

Case $1:$ All $3$ letters are district

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 rearranged in $\frac{3!}{2!}$ ways.

Total $=2\times 3\times 3=18$

$\therefore$ Required $=24+18=42$ words.

Hence, the answer is $42.$