Question

The number of $4$ letter words (with or without meaning) that can be made from the eleven letters of the word “EXAMINATION” is

Answer 1

Find the number of words

Total number of different alphabet $8$

$\Rightarrow$Case I: All different alphabets are selected

Number of words formed $={}^8{C}_4\times 4!=1680$

$\Rightarrow$Case II: $2$ alphabet are same and $2$ are different

Number of words formed $={}^{3}C_1\times {}^7{C}_2\times \left(\frac{4!}{2!}\right)=756$

$\Rightarrow$Case III: $2$ pair of alphabet are same

Number of words formed $={}^3{C}_2\times \frac{4!}{2!2!}=18$

Total number of word formed $=1680+756+18=2454$

Hence, total number of word formed is $2454$.