Question

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

Answer 1

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`