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1.  
0! + 1! + 2! + 3! = ?

Correct Answer: D [10]

Explanation:

1 + 1 + 2 + 6 = 10.

2.  
In how many ways can a president and a secretary be chosen from 8 members (one person cannot hold both posts)?

Correct Answer: A [56]

Explanation:

Order matters: ⁸P₂ = 8 × 7 = 56.

3.  
A coin is tossed and a die is thrown. The probability of a head and an even number is:

Correct Answer: B [1/4]

Explanation:

1/2 × 1/2 = 1/4.

4.  
How many 4-letter codes can be made from the letters A, B and C if letters may repeat?

Correct Answer: C [81]

Explanation:

3 × 3 × 3 × 3 = 81.

5.  
A card is drawn from a pack of 52. The probability that it is a black card or an ace is:

Correct Answer: E [7/13]

Explanation:

26 black + 4 aces − 2 black aces = 28 → 28/52 = 7/13.

6.  
In how many different ways can the letters of the word LEVEL be arranged?

Correct Answer: D [30]

Explanation:

5!/(2! × 2!) = 30.

7.  
In how many ways can 8 different beads be strung into a necklace?

Correct Answer: A [2,520]

Explanation:

(8 − 1)!/2 = 5,040/2 = 2,520 (a necklace can be turned over).

8.  
Two dice are thrown. The probability that the sum is a prime number is:

Correct Answer: C [5/12]

Explanation:

Sums 2, 3, 5, 7, 11 → 1 + 2 + 4 + 6 + 2 = 15 ways → 15/36 = 5/12.

9.  
What is the sum of all the 3-digit numbers that can be formed with the digits 2, 4 and 6, each used once?

Correct Answer: B [2,664]

Explanation:

Each digit appears twice in each place: 2!

10.  
How many positive divisors does 72 have?

Correct Answer: D [12]

Explanation:

72 = 2³ × 3² → (3 + 1)(2 + 1) = 12.

11.  
How many 4-digit numbers with all digits different can be formed from 0, 1, 2, 3, 4?

Correct Answer: A [96]

Explanation:

First digit 4 ways (not 0), then 4 × 3 × 2 → 96.

12.  
In how many ways can a student pick at least one book from 4 different books?

Correct Answer: B [15]

Explanation:

2⁴ − 1 = 15 (each book in or out, minus none).

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