Official solution
Case 1 :
When all the four letters different then no of words
= 5C4 \[ \times \]4!
Case 2 :
When out of four letters two letters are R and other two different letters are chosen from B, A, C, K then the no of words
= 4C2 \[ \times \] \[{{4!} \over {2!}}\] = 72
Case 3 :
When out of four letters two letters are A and other two different letters are chosen from B, R, C, K then the no of words
= 4C2 \[ \times \] \[{{4!} \over {2!}}\] = 72
Case 4 :
When word is formed using two R and two A then number of words
= \[{{4!} \over {2!2!}}\] = 6
So, total number of 4 letters words possible = 120 + 72 + 72 + 6 = 270