Math 70 Spring 2022
Assignment 5 due Monday, December 12, 2022
1. (3 points) Let E !à”à#àand define J E E by the formula J +`+$ ? + -od $^
Find J . Is J one-to-one? Is J onto? Explain. Is J

?
2. (3 points) How many integers between 1 and “*** are multiples of $ or &?
3. (3 points each) Suppose the set E has 8
” elements and the set F has 7
” elements.
(a) How many functions 0 E F are possible?
(b) How many functions 1 F E are possible?
(c) If 8 7, how many one-to-one onto functions are possible?
Problem 4, 5, and 6 are the counting problems. All questions in these problems ask you for the
number of objects or ways. Leave your answers in formula form, such as ? $# ?. Ask yourself: Is
order important? Are repeats possible?
4. (2 points each) Berkeley physics grad students challenge the MIT physics grad students to a
Thanksgiving Physics Smart-Off Contest. Each school is allowed to choose 4 grad students.
(a) If Berkeley has 20 Physics grad students and MIT has 21 Physics grad students, how many
different way can the contestants be chosen?
(b) Suppose each team must choose at least one female grad student. Berkeley has 9 female Physics
grad students and MIT has 8 female Physics grad students,
5. (2 points each) An instructor consults www.ezfinal.com’s web page which contains 14 questions that
would fit the material cover in the class.
(a) In how many ways can he select 10 questions for his final?
(b) Suppose 6 of the 14 questions require proofs, the others do not, in how many ways can he select 4
the require proofs and 6 that do not?
6. (2 points) A large pile of coins consisting of pennies, nickels, dimes, and quarters (at least 20 of each).
How many different collections of 20 coins can be chosen?

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