Please answer the following questions in the attached image (Course: discrete structures and combination analysis) :

3. (3)arks) Find the number of solutions to x+y+z=32, where x,y and z are nonnegative integers such that x7 and y15. 4. (4 marks) Find a recurrence relation for the number of decimal strings (strings made up of decimal digits) of length n that do not contain three consecutive 9s. What are the initial conditions? Explain your answer. length n decinal=098tringsthathavea5=10gn=9an1+9an2+9an3+10n3 Btringsthathavea5 trings that do not contain 3 cons. 95 anan=10n9n1+an2+aa Sminal Conditions