Question

permutations are there with people)? 34. A class has enough time for 4 questions. 10 students are present. Suppose a student can ask up to 4 questions, how many combinations can there be of students asking questions? (How many 4- combinations are there from 10 students, with repetition)? 35. Show that if there are 30 students in a class, then at least two of the students have first names that 3pts begin with the same letter. What principle can you apply? 3pts 36. Apply the binomial theorem to find the coefficient of x'y2 for (2x-3y)" 4pts Solve for the following. Simplify and find the integer. Show all work. 37. P(7,6) = 38. C(10,8) = 3pts procedure factorial (n: nonnegative integer) if n=0 then return 1 else return n factorial(n-1) Given the recursive algorithm above, give the output of factorial(4), showing all recursive calls: 2pts procedure rec_func(n: positive integer) if n = 1 then return 1 else return n + rec_func(n-1) 40. What does this algorithm compute? a. Product of the first n positive integers b. Sum of the first n positive integers c. Factorial of the first n positive integers d. The answer tonn-1 14 24 14 36 27 10

Answer 1

36.

Coefficient = 4C2 * (2)² * (-3)² = 6 * 4 * 9 = 216

37. P(7, 6) = 7! / (7-6)! = 5040

38. C(10, 8) = 10!/ [(10-8)! * 8!] = 10!/(2! * 8!) = 10 * 9 / 2 = 45

39.

factorial(4) = 4 * factorial(3) = 4 * 3 * factorial(2) = 4 * 3 * 2 * factorial(1) = 4 * 3 * 2 * 1 * factorial(0)

= 4 * 3 * 2 * 1 * 1

= 24

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