2018 AMC 10B Problems/Problem 5
Problem
How many subsets of contain at least one prime number?
Solution
Consider finding the number of subsets that do not contain any primes. There are four primes in the set: , , , and . This means that the number of subsets without any primes is the number of subsets of , which is just . The number of subsets with at least one prime is the number of subsets minus the number of subsets without any primes. The number of subsets is . Thus, the answer is .
See Also
2018 AMC 10B (Problems • Answer Key • Resources) | ||
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Followed by Problem 5 | |
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