Question

The number of four letter words that can be formed using the letters of the word $BARRACK$ is

• A. $120$
• B. $270$
• C. $264$
• D. $144$

Answer 1

The correct option is B $270$

Case $1:$
If all four letters are different, then the number of words $={}^5{C}_4\times 4!=120$

Case $2:$
If two letters are of same kind and others are different, then the number of words $={}^2{C}_1\times {}^4{C}_2\times \frac{4!}{2!}=144$

Case $3:$
If first two are same letters and second two are also same letters, then the number of words $=\frac{4!}{2!2!}=6$

Hence, total number of words $=120+144+6=270$