Discrete Mathematics Practice Test 7

1. What is the generating function for the generating sequence A = 1, 9, 25, 49,…?

2. If a fair 15-sided dice is rolled, then is the probability that the roll is an odd number or prime number or both?

3. What is the generating function for generating series 1, 2, 3, 4, 5,… ?

4. What is the sequence depicted by the generating series 4 + 15x² + 10x³ + 25x⁵ + 16x⁶+⋯?

5. In class, students want to join sports. 15 people will join football, 24 people will join basketball, and 7 people will join both. How many people are there in the class?

6. Determine the coefficient of the x⁵y⁷ term in the polynomial expansion of (m+n)¹².

7. A meeting has 12 employees. Given that 8 of the employees is a woman, find the probability that all the employees are women?

8. The explicit formula for the geometric sequence 3, 15, 75, 375,... is _______

9. _________ number of reflexive relations are there on a set of 11 distinct elements.

10. A box consists of 5 yellow, 12 red and 8 blue balls. If 5 balls are drawn from this box one after the other without replacement, find the probability that the 5 balls are all yellow balls.