PFA

PFA


* * CPU Business and Information Technology College Department of Computer Science Discrete Mathematics and Combinatory Assignment Submission date: January 13, 2020 Attempt each of the following questions and show all the necessary steps clearly and briefly. 1. There are 7 boys and 3 girls in a gathering. In how many ways can they be arranged in a row, so that the 3 girls form a single block? 2. Find the value of ? so that ∑ (50 ? )8?50?=0 = ? 100 . 3. An employee joined a company in 1987 with a starting salary of 50, 000. Every year this employee receives a raise of 1000 plus 5% of the salary of the previous year. Then a) Find a recurrence relation for the salary of this employee ? years after 1987. b) Find an explicit formula for the salary of this employee ? years after 1987. c) What is the salary of this employee in 1995? 4. Find the order of a graph of size 45 with seven vertices of degree 6, five vertices of degree 4 and the remaining vertices of degree 7. 5. Draw a self complementary graph of order 8. 6. In a company, there are 50 employees and some committees. If each employee belongs to 6 committees and each committee consists of 10 people, how many committees are there?