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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
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`
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