Ministry of Higher Education Kingdom of Saudi Arabia CSTS SEU, KSA Discrete Mathematics-MATH 150 ASSIGNMENT-3 2nd Semester 2016-17 Section-I (1 mark for each) State whether the following statements are true or false1. Mathematical induction, strong induction and well ordering are not equivalent principles. 2. is a linear homogeneous recurrence relation 3. ( ) ( ) 4. The Basis Step in Mathematical Induction is \"Show that P(1) is true , n .\" 5. If 16 objects are placed into 15 boxes, then there is at least one box containing 3 objects. 6. The first five Fibonacci numbers are: 1,1, 2,3,5,8. 1 2 3 4 5 1 6 Ministry of Higher Education Kingdom of Saudi Arabia CSTS SEU, KSA Section-II (1 mark for each) Select one of the alternatives from the following questions as your answer1. permutations of the letters ABCD is equal A. 24 B. 12 C. 4 D. 6 2. is defined recursively by integers n, then is A. B. C. D. 12 6 3 2 3. The coecient of x4y3 in the expansion of (x + y)7 is A. 21 B. 30 C. 32 D. 35 4. If A. B. C. D. ( 0 1 3 5 ) , then the value of 5. The characteristic equation of the recurrence relation is obtained by substituting A. B. 2 for positive Ministry of Higher Education Kingdom of Saudi Arabia CSTS SEU, KSA C. D. 6. The roots of a characteristic equation of a linear homogeneous recurrence relation are . The general solution of the recurrence relation is in the form A. B. C. D. 1 2 3 ANSWER 3 4 5 6 Ministry of Higher Education Kingdom of Saudi Arabia CSTS SEU, KSA Section-III (3 marks for each) Solve the following questions 1. Use mathematical induction to show that . 2. There are 7 juniors and 9 seniors in a Service Club. The club wants to send 5 representatives to a Conference. a) How many ways are there to select 2 juniors and 3 seniors b) How many ways are there to select the chairman from the seniors, and the rest are juniors 4 Ministry of Higher Education Kingdom of Saudi Arabia CSTS SEU, KSA 3. Find the first 3 terms in the expansion of ( ) . 4. Find the general solution of the recurrence relation , with a0 = 2, and a1 = 5. 5 Ministry of Higher Education Kingdom of Saudi Arabia 5. Find ( ) ( ) ( ) ( ) and and for ( ) b. ( ) a. CSTS SEU, KSA ( ), if ( ) is defined recursively by ( ) ( ) . 6. Somebody can choose pictures from four lists. The four lists contain 18, 6,12,4 pictures respectively. There is no picture is on more than one list. How many possible ways can choose 4 pictures by select one picture from each list Good luck 6