# Letters of the word MOTHER are arranged at random. Find the probability that in the arrangement O is at the begining and end with T - Mathematics and Statistics

Sum

Letters of the word MOTHER are arranged at random. Find the probability that in the arrangement O is at the begining and end with T

#### Solution

There are 6 letters in the word MOTHER.

These letters can be arranged among themselves in 6P6 = 6! ways.

∴ n(S) = 6!

Let event C: Word begins with O and ends with T.
Thus first and last, letters can be arranged in one way each, and the remaining 4 letters can be arranged in 4P4 = 4! ways

∴ n(C) = 4! × 1 × 1 = 4!

∴ P(C) = ("n"("C"))/("n"("S"))

= (4!)/(6!)

= 1/30

Concept: Concept of Probability
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