If the letters of the world mathematics are arranged arbitrarily,the probability that C comes beforeE and E beforeH and H - Maths - Probability

Question

If the letters of the world mathematics are arranged
arbitrarily,the probability that C comes beforeE and E beforeH and
H before I and I before S is ?

Aarushi Mishra · Accepted Answer

M A T H E M A T I C STotal no
 of words=11Arrrangement of n things if, r1 things of one type are alike, r2 things of other type are alike and so on upto rk=n!r1! r2! r3!
rkOrder of letter C E H I and S are fixed, i
e
 they are not interchanged among themselves during arranging
 They can be treated as if they are alikeThere are 2 A's2M's2T'sAnd letters C, E, H, I and S are considered identicalTotal number of ways of aranging=11!2! 2! 2! 5!total number of of ways of arranging letters=11!2! 2! 2!Pprobability that C comes before E and E before H and H before I and I before S=no
 of favourable outcomestotal number of outcomes=11!2! 2! 2! 5!11!2! 2! 2!=15!=1120

If the letters of the world mathematics are arranged arbitrarily,the probability that C comes beforeE and E beforeH and H before I and I before S is.?