- (A) 120,960
- (B) 181,440
- (C) 45,360
- (D) 30,240
Q2: How many distinct permutations of the set { 1, 2, 3, 4, 5, 6, 7, 8, 9 } are there if the elements must be arranged such that all odd numbers appear before all even numbers?
- (A) 9!
- (B) 4! × 5!
- (C) 5! × 4!
- (D) 8!
Q3: How many ways can we choose a committee of 3 people from a group of 8 men and 7 women, if the committee must consist of at least 2 women?
- (A) 455
- (B) 315
- (C) 380
- (D) 210
Q4: In a bipartite graph with 5 vertices in one set and 6 vertices in another, how many edges can the graph have at maximum?
- (A) 25
- (B) 30
- (C) 60
- (D) 15
Q5: How many different ways can we color the edges of a complete graph K₄ with 3 colors, such that no two edges that share a common vertex have the same color?
- (A) 18
- (B) 27
- (C) 81
- (D) 72
Q6: How many ways can we select a subset of 5 elements from a set of 12 elements such that at least 3 elements are from the first 6 elements of the set?
- (A) 1,350
- (B) 1,200
- (C) 1,000
- (D) 900
Q7: How many ways can you arrange the letters of the word “DISCRETE” such that no two vowels are adjacent?
- (A) 144
- (B) 288
- (C) 432
- (D) 720
Q8: What is the number of distinct 5-digit numbers that can be formed using the digits 1, 2, 3, 4, and 5, with repetition allowed, if the number must be divisible by 5?
- (A) 125
- (B) 625
- (C) 312
- (D) 250
Q9: How many different ways can we arrange the digits of the number “2001” such that the resulting number is divisible by 4?
- (A) 3
- (B) 6
- (C) 4
- (D) 2
Q10: How many ways can we select a group of 5 students from a class of 12 students, if the group must have at least one student from each of the three available sections?
- (A) 2,500
- (B) 1,800
- (C) 2,000
- (D) 1,000