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

Question

Aicharya · Accepted Answer

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

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

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