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Questions below followed by three quantities. Find the relationship between them. Quantity I: In how many ways the letter of the word ‘MANUAL’ can be arranged so that vowels come together? Quantity II: Find the number of ways of forming a five number Team for a project from a group of 6 workers and 5 managers such that no odd numbers of managers are selected in the project? Quantity III: The letters of the word NATURE are to be arranged so that three vowels should not come together. Find the number of arrangement.

Questions below followed by three quantities. Find the relationship between them. Quantity I: In how many ways the letter of the word ‘MANUAL’ can be arranged so that vowels come together? Quantity II: Find the number of ways of forming a five number Team for a project from a group of 6 workers and 5 managers such that no odd numbers of managers are selected in the project? Quantity III: The letters of the word NATURE are to be arranged so that three vowels should not come together. Find the number of arrangement. Correct Answer Quantity I < Quantity II < Quantity III

Quantity I:

MANUAL = (MNL) (AUA)

Number of arrangement,

⇒ (4! × 3!)/2!

⇒ 72

Quantity II:

Possible cases = (3W 2M) (1W 4M)

⇒ 6C3 × 5C2 + 6C1 × 5C4

⇒ 200 + 30 = 230

Quantity III:

Total letters = 6

Number of vowels = 3 (AUE)

Number of words when three vowels come together = AUE NTR

⇒ 4! × 3!

Required arrangement = 6! - (4! × 3!) = 720 - 144 = 576

Quantity I < Quantity II < Quantity III

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