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1.  
In how many arrangements of the letters of the word ORANGE are no two vowels next to each other?

Correct Answer: C [144]

Explanation:

Place R, N, G first: 3! = 6; vowels O, A, E go into 3 of the 4 gaps: ⁴P₃ = 24 → 6 × 24 = 144.

2.  
A committee of 4 is to be chosen from 6 men and 5 women. In how many ways can it include at least 2 women?

Correct Answer: E [215]

Explanation:

Total ¹¹C₄ = 330; subtract no woman (⁶C₄ = 15) and exactly one woman (5 × ⁶C₃ = 100) → 215.

3.  
In how many arrangements of the letters of the word ARTICLE do the vowels occupy only the even places (2nd, 4th, 6th)?

Correct Answer: B [144]

Explanation:

3 vowels A, I, E fill the 3 even places in 3!

4.  
Quantity I: The probability that the sum is 8 when two dice are thrown.
Quantity II: The probability that a card drawn from a pack of 52 is a king or a queen.

Correct Answer: B [Quantity I < Quantity II]

Explanation:

I: 5/36 ≈ 0.139. II: 8/52 = 2/13 ≈ 0.154.

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