Question

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

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

Answer 1

Answer: (D)

$270$

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

Case 2: If 2 letters are R and other 2 different letters are chosen from B, A, C, K then the number of words ${=}^4{C}_2\times \frac{4!}{2!}=72$

Case 3: If 2 letters are A and other 2 different letters are chosen from B,R,C,K then the number of words ${=}^4{C}_2\times \frac{4!}{2!}=72$

Case 4: when word is formed using $2R^{\prime }s$ and $2A^{\prime }s$$=\frac{4!}{2!2!}=6$

Then the number of four-letter words that can be formed$=120+72+72+6=270$