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Question: descrete structures questions 1 2 and 3 please...

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Descrete Structures
Smith MTH 225 Discrete Structures 1 Homework Assignment 1 Sections 0.3 and 1.1 Your descriptions of your algorithms or reasoning for counting each set of desired outcomes is as important as the final result of the calculations. 1. A restaurant has 3 appetizers, 7 main dishes, and 2 desserts a) How many ways can you order 1 item? b) How many ways can you order two items from different categories? c) How many ways can you order three items from different categories? d) How many ways can you order up to three items from different categories? 2. How many integers between 1 and 5000 (inclusive) are not divisible by any of 2,3, or 5? 3. Let Q be the set of 7-digit strings (order matters) using digits 0-9 with no repeated digits. a) What is the cardinality of Q? b) How many strings in Q contain a 3? c) How many strings in Q contain a 3 and a 5? d) How many strings in @ contain a 4 or a 6, but not both? Two students are working on a problem that asks them to count 3-digit strings using 0-9, with repetition allowed, where at least one of the digits is a 1. Unfortunately, each student has an error in their reasoning 4. Questions 1, 2 and 3 please
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