Class 11

Math

Algebra

Permutations and Combinations

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

- $144$
- $120$
- $264$
- $270$

Case 2: If 2 letters are R and other 2 different letters are chosen from B, A, C, K then the number of words $=_{4}C_{2}×2!4! =72$

Case 3: If 2 letters are A and other 2 different letters are chosen from B,R,C,K then the number of words $=_{4}C_{2}×2!4! =72$

Case 4: when word is formed using $2R_{′}s$ and $2A_{′}s$$=2!2!4! =6$

Then the number of four-letter words that can be formed$=120+72+72+6=270$