Name: MATH 140 - Lecture 10 Homework Section: 1. From a standard deck of 52 cards, how many 5-card poker hands are there, that have at least use 3 spades? (Hint: divide the problem in cases: a poker hand has 3 spades, 4 spades, 5 spades.) cares 2. Show the following propositions using a direct proof, using cases. (a) Proposition. If n E Z, then 5n² + 3n +7 is odd. (b) Proposition. If two integers have the same parity, then their sum is even.

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1. From a standard deck of 52 cards, how many 5 -card poker hands are there, that have at least wse 3 spades? (Hint: divide the problem in cases: a poker hand has 3 spades, 4 spades, 5 spades.) cares 2. Show the following propositions using a direct proof, using cases. (a) Proposition. If

n \in Z

, then

5 n^{2} + 3 n + 7

is odd. (b) Proposition. If two integers have the same parity, then their sum is even.

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