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

JEE · Math · previous-year question

  1. A.120
  2. B.144
  3. C.264
  4. D.270correct

Answer

D. 270

Explanation

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

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