The number of four letter words that can be formed using the letters of the word BARRACK is
The number of four letter words that can be formed using the letters of the word BARRACK is
144
120
264
270
Solution
If all four letters are different then the number of words ${ }^5 \mathrm{C}_4 \times 4 !=120$
If two letters are $\mathrm{R}$ and other two different letters are chosen from $\mathrm{B}, \mathrm{A}, \mathrm{C}, \mathrm{K}$ then the number of words $={ }^4 \mathrm{C}_2 \times \frac{4 !}{2 !}=72$
If two letters are $\mathrm{A}$ and other two different letters are chosen from $\mathrm{B}, \mathrm{R}, \mathrm{C}, \mathrm{K}$ then the number of words $={ }^4 \mathrm{C}_2 \times \frac{4 !}{2 !}=72$
If word is formed using two $R$ 's and two $A$ 's then the number of words $=\frac{4 !}{2 ! 2 !}=6$
Therefore, the number of four-letter words that can be formed $=120+72+72+6=270$