Question

The letters of the word LOGARITHM are arranged at random. Find the probability that Begins with O and ends with T.

Answer 1

There are 9 letters in the word LOGARITHM.
These letters can be arranged among themselves in ⁹P₉ = 9! ways.
∴ n(S) = 9!
Let D be the event that word begins with O and ends with T.
Thus first and the last letter can be arranged in one way each and the remaining 7 letters can be arranged in the remaining 7 places in ⁷P₇ = 7! ways
∴ n(D) =  1 × 7! × 1 = 7!

∴ P(D) = `("n"("D"))/("n"("S")`

= `(7!)/(9!)`