Lets first take care of the denominator The letters of word "SOCIETY can be arranged in 7! ways.

Numerator : lets get them all vowels together OIE and others SCTY. lets keep them vowels togethe, so then, if we name vowels as V we get, VSCTY which can be arranged in 5! and the vowels can be arranged within themselves in 3! ways. Altogether, we get \(\frac{5!3!}{7!}\) which reduces to \(\frac{1}{7}\)

Hence Answer E. IMO

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