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प्रश्न
The letters of the word LOGARITHM are arranged at random. Find the probability that vowels are always together.
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उत्तर
There are 9 letters in the word LOGARITHM.
These letters can be arranged among themselves in 9P9 = 9! ways.
∴ n(S) = 9!
Let A be the event that vowels are always together.
The word LOGARITHM consists of 3 vowels (O, A, I) and 6 consonants (L, G, R, T, H, M).
3 vowels can be arranged among themselves in = 3P3 = 3! ways.
Considering 3 vowels as one group, 6 consonants and this group (i.e., altogether 7) can be arranged in 7P7 = 7! ways.
∴ n(A) = 7! × 3!
∴ P(A) = `("n"("A"))/("n"("S"))`
= `(7!xx3!)/(9!)`
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