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प्रश्न
Determine the number of arrangements of letters of the word ALGORITHM if no two vowels are together.
उत्तर
There are 6 consonants in the word ALGORITHM.
They can be arranged among themselves in 6P6 i.e., 6! ways.
Let consonants be denoted by C.
_ C _ C _ C _ C _ C _ C _
There are 7 places marked by “______” in which 3 vowels are to be arranged.
∴ Vowels can be arranged in 7P3
= `(7!)/((7-3)!)`
= `(7xx6xx5xx4!)/(4!)`
= 210 ways
∴ Required number of arrangements
= 6! × 210 = 720 × 210 = 151200
∴ 151200 words can be formed if no two vowels are together.
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