The number of words can be formed with the letters of the word 'MATHEMATICS' by rearranging them, is

Options

A. `6*7*.^(8)C_(4)`
B. `6*8*.^(7)C_(4)`
C. `7*.^(6)C_(4)*.^(8)C_(4)`
D. `8*.^(6)C_(4)*.^(7)C_(4)`

Answer

C

Explanation

Other than S seve letters M,I,I,I,P,P,I can be arranged in `(7!)/(2!4!)=(7*6*5)/(1*2)=7*.^(6)C_(2)=7*.^(6)C_(4)`
now, four S can be placed in 8 spaces in `.^(8)C_(4)` ways.
hence, required number of ways`=7*.^(6)C_(4)*.^(8)C_(4)`.