МCBSМАT 255Note: For Problems 3 and 4, you may use the following two facts about the Euler Phi-function:a) If integers m and n are coprime, then o(mn) = ¢(m)o(n).b) If p is a prime number and a is a positive integer, then o(p") = pª-1(p – 1)1. In a class of 16 students, there are 6 male students and 10 female students. In how many ways canyou select a group of 5 students from this class such that 3 of the 5 students are males and the othertwo are females?2. Use the inclusion-exclusion principle to find the number of solutions to the equationx + y + z = 19,where x, y, and z are positive integers. [Hint: You know how to find the number of non-negativesolutions to the equation above.]3. Let ø: {1, 2, 3, ...} → {1, 2, 3, ...} denote the Euler phi-function. If ø injective? Is it surjective? Justifyyour answers.4. Define a relation - on the set N of natural numbers as follows: For natural numbers n and m, n ~ m ifand only if ø(n) = ¢(m), where o denotes the Euler phi-function. Is ~ defined as such an equivalencerelation on N? If so, find the equivalence class containing 5.5. Let S be a set containing 8 elements. What is the number of subsets of S containing at least twoelements? Justify your answer.

Name: МCBSМАT 255Note: For Problems 3 and 4, you may use the following two
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Description: МCBSМАT 255Note: For Problems 3 and 4, you may use the following two facts about the Euler Phi-function:a) If integers m and n are coprime, then o(mn) = ¢(m)o(n).b) If p is a prime number and a is a positive integer, then o(p") = pª-1(p – 1)1. In a

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In a class of 16 students, there are 6 male students and 10 female students. In how many ways can you select a group of 5 students from this class such that 3 of the 5 students are males and the other two are females?

In a class of 16 students, there are 6 male students and 10 female students. In how many ways can you select a group of 5 students from this class such that 3 of the 5 students are males and the other two are females?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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