Question

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

• A. $\frac{1}{75}$
• B. $\frac{1}{24}$
• C. $\frac{1}{120}$
• D. $\frac{1}{7920}$

Answer 1

The correct option is D $\frac{1}{7920}$

Given wold is MATHEMATICS $\Rightarrow 11$ character

no. of m's = no.of A's = no.of T's = 2

$\therefore$ Total possible outcomes $=\frac{11!}{2!2!2!}$

For c to cone before E, E before H, H before I, I before s,

we should consider 'CEHIS' as 1 character,

where in the order of 5 character can't be changed.

Total no.of possible outcomes with given condition

$\Rightarrow \frac{7!}{2!2!2!}$

$\therefore$ Probability with given condition $=\left(\frac{7!}{2!2!2!}\right)\left(\frac{11!}{2!2!2!}\right)$

$=\frac{1}{7920}$