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

Step-by-step solution

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