Question

Find the number of selections and of arrangements that can be made by taking $4$ letters from the word expression.

Answer 1

$⟹$ Total number of letters $=10$
$\underset{–}{ee}$ $\underset{–}{x}$ $\underset{–}{p}$ $\underset{–}{r}$ $\underset{–}{ss}$ $\underset{–}{i}$ $\underset{–}{o}$ $\underset{–}{n}$
Double letters bundles $=2$
Single letters $=6+2=8$ ( 1-e, 1-s)
Possible ways of selection include:-
All $4$ from single $={}^8{C}_4=70$
$2$ from single $1$ from double $={}^7{C}_2\times {}^2{C}_1=42$
$2$ from double $={}^2{C}_2=1$
Total Selections $=113$
Number of arrangements:-
All from single $={}^8{C}_4\times 4!=1680$
$2$ from single $1$ from double $={}^7{C}_2\times {}^2{C}_1\times \frac{4!}{2!}=504$
$2$ from double $={}^2{C}_2\times \frac{4!}{2!2!}=6$
Total $=2190$