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In the following question, two statements are numbered as I and II. On solving these statements, we get quantities I and II respectively. Solve for the both quantities and choose the correct option. 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.

In the following question, two statements are numbered as I and II. On solving these statements, we get quantities I and II respectively. Solve for the both quantities and choose the correct option. 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. Correct Answer Quantity I < Quantity II

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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