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

Step-by-step solution

If all four letters are different then the number of words ^5 C ₄ 4 !=120 If two letters are R and other two different letters are chosen from B , A , C , K then the number of words = ^4 C ₂ 4 ! 2 ! =72 If two letters are A and other two different letters are chosen from B , R , C , K then the number of words = ^4 C ₂ 4 ! 2 ! =72 If word is formed using two R 's and two A 's then the number of words = 4 ! 2 ! 2 ! =6 Therefore, the number of four-letter words that can be formed =120+72+72+6=270