The number of four letter words that can be formed using the...

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 $=120+72+72+6=270$