JEE MAIN - Mathematics (2018 - 15th April Evening Slot - No. 4)
The number of four letter words that can be formed using the letters of the word BARRACK is :
120
144
264
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
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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