Mathematics - Permutation & Combination Question with Solution | TestHub

Other than $\mathrm{S}$, seven letters $\mathrm{M},\mathrm{I},\mathrm{I},\mathrm{I},\mathrm{P},\mathrm{P},\mathrm{I}$ can be arranged in $\frac{7!}{2!4!}=\mathrm{7.5.3}$. Now four $\mathrm{S}$ can be placed in 8 spaces in ${}^8{\mathrm{C}}_4$ ways. Desired number of ways $=7.5\cdot 3\cdot {}^8{\mathrm{C}}_4=7\cdot {}^6{\mathrm{C}}_4\cdot {}^8{\mathrm{C}}_4$