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प्रश्न
Letters of the word MOTHER are arranged at random. Find the probability that in the arrangement vowels are always together.
उत्तर
There are 6 letters in the word MOTHER.
These letters can be arranged among themselves in 6P6 = 6! ways.
∴ n(S) = 6!
Let event A: Vowels are always together.
The word MOTHER consists of 2 vowels (O, E) and 4 consonants (M, T, H, R).
2 vowels can be arranged among themselves in 2P2 = 2! ways.
Let us consider 2 vowels as one group. This one group with 4 consonants can be arranged in 5P5 = 5! ways.
∴ n(A) = 2! × 5!
∴ P(A) = `("n"("A"))/("n"("S"))`
= `(2! xx 5!)/(6!)`
= `1/3`
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