Quantity I – In how many ways letters of MOBILE can be arranged when vowels are always together.
Quantity II – In how many ways letters of MONDAY can be arranged when vowels are not together.
Quantity I: Required no. of ways = 3! × 4! = 6 × 24 = 144 Quantity II. Total no. of ways = 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720 No. of ways when vowels are always together = 2! × 5! = 2 × 120 = 240 No. of ways when vowels are not together = 720 – 240 = 480 ∴ Quantity I < Quantity II.
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