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 $270$

Case1:
If all four letters are different then number of words $={}^5{C}_4\times 4!=120$
Case2:
If two letters are of same kind and others are different then numbers of words $={}^2{C}_1\cdot {}^4{C}_2\frac{4!}{2!}=144$
Case3:
If first two are same letters and second two are also same letters then number of words $=\frac{4!}{2!2!}=6$
Hence, Total number of words $=120+144+6=270$