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

The total numbers of arrangements is 11!2!2!2!=11!8 The number of arrangements in which C, E, H, I, S appear in  that order 11C56!2!2!2!=11!8⋅5!∴ Required Probability =11!8⋅5!11!8=1120