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How many subsets of {0, 1, ...,9} have cardinality 5 or more?

How many subsets of {0, 1, ...,9} have cardinality 5 or more?

Advanced Engineering Mathematics
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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Discrete Math: Binomial Coefficients

**Question:** How many subsets of \(\{0, 1, \ldots, 9\}\) have cardinality 5 or more? **Explanation:** There is a text box below the question, which is intended for the user to input their answer. The question is asking for the number of subsets of the set \(\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}\) that have 5 or more elements. The cardinality refers to the number of elements in a subset. To solve this problem, you need to calculate the number of subsets with cardinalities 5, 6, 7, 8, 9, and 10, and then sum these numbers. This can be done using combinations, where the combination formula \(\binom{n}{k}\) represents the number of ways to choose \(k\) elements from \(n\) elements.
Transcribed Image Text:**Question:** How many subsets of \(\{0, 1, \ldots, 9\}\) have cardinality 5 or more? **Explanation:** There is a text box below the question, which is intended for the user to input their answer. The question is asking for the number of subsets of the set \(\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}\) that have 5 or more elements. The cardinality refers to the number of elements in a subset. To solve this problem, you need to calculate the number of subsets with cardinalities 5, 6, 7, 8, 9, and 10, and then sum these numbers. This can be done using combinations, where the combination formula \(\binom{n}{k}\) represents the number of ways to choose \(k\) elements from \(n\) elements.
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