Question

Find the number of $3$ letter words that can be formed from the word ${}^{\prime }SERIE{S}^{\prime }$.

Answer 1

There are four distinct letters in world SERIES (SERI)

we can either use three of the four letters or use two of the four letters or by using S or E twice.

choosing 3 distinct letters in ${}^4{P}_3=4\times 3\times 2=24$ ways

$\to$ we can choose exactly two letters if you use S or E twice

Thus, there are ${}^2{C}_1$ ways of choosing the repeated letter.

${}^3{C}_2$ ways of choosing where to place those letters in 3 letter word and in ${}^3{C}_1$ ways of choosing 3rd letter in the word,

Thus,

${}^2{C}_1{\times }^3{C}_2{\times }^3{C}_1=2\times 3\times 3=18$ ways to find/ form a word with repeated letter.

Thus,

there are 24+18 = 42 distinguishable three letter words that can be formed.