If the letters of the word MATHEMATICS are arranged arbitrarily, the probability that C comes before E, E before H, H before I and I before S, is

Options

A. `(1)/(75)`
B. `(1)/(24)`
C. `(1)/(120)`
D. `(1)/(720)`

Answer

C

Explanation

`(c )` The total number of arrangments is `(11!)/(2!2!2!)=(11!)/(8)`
The number of arrangements in which `CE,H,I,S` appear in that order `"^(11)C_(5)(6!)/(2!2!2!)=(11!)/(8*5!)`
`:.` Required Proability `=((11!)/(8*5!))/((11!)/(8))=(1)/(120)`