There are 7 letters in the word SOCIETY. ∴ Total number of ways of arranging all the 7 letters = n(S) = 7!. When the case of three vowels being together is taken, then the three vowels are considered as one unit, so the number of ways in which 5 letters (SCTY–4, IEO–1) can be arranged = 5!Also the 3 vowels can be arranged amongst themselves in 3! ways ∴ Total number of favourable cases = 5! × 3! ∴ Required probability = \(rac{5! imes3!}{7!}\) = \(rac{1}{7}\)