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

Word BARRACK has 7 letters in which 'A' and ' \(R\) ' repeats twice.
Case I :
All four letters are different. (B, A, R, C, K)
\(\therefore\) No. of letters \(={ }^5 \mathrm{C}_4 \times 4!=120\)
Case II :
'\(R\)' repeats twice and remaining letter three letters are different (B, A, C, K)
\(\therefore\) No. of letters \(={ }^4 \mathrm{C}_2 \times \frac{4!}{2!}=72\)
Case III :
'A' repeats twice and remaining letter three letters are different (B, R, C, K)
\(\therefore\) No. of letters \(={ }^4 \mathrm{C}_2 \times \frac{4!}{2!}=72\)
Case IV :
Both 'A' and 'R' repeat twice.
\(\therefore\) No. of letters \(=\frac{4!}{2!2!}=6\)
\(\therefore\) Total no. of letters form \(=120+72+72+6\)
\(=270\)