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Unformatted text preview: Practice problems for Midterm II. Sets and combinatorics (Chapter 2.1) 1. How many 3-element subsets are there in the set with 10 elements? 2. A set A is a subset of B . How many subsets of B do not intersect A , if | A | = k, | B | = n ? 3. In a lottery, a player should pick five different numbers from 1 to 56 and one number from 1 to 46. How many different sequences of 6 numbers can he get? 4. Seven teams participate in a tournament, each two of them should play once. How many games will be played? 5. How many diagonals can be drawn in a convex n-gon? 6. A phone number contains 7 digits and cannot start from 0. How many different phone numbers can be assigned? 7. In a college everyone studies Greek, Latin or both languages. 85% of students study Greek, 70% study Latin. How many students study both? Functions and relations (Chapters 2.2-2.3) 8. Construct a function from a line to a circle that is a) Surjective b) Injective c)** Bijective 9. Consider the set of stations of the Long Island Rail Road. Define the9....
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