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five people plan to meet after school, and if they all show up, there will be one group of five people. How many possible subsets of any size are there?

User Kreuzberg
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1 Answer

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Answer:

If there are 5 people meeting after school, and they will form 1 group of 5 people if everyone shows up, then there are:

1 subset of 5 people (the full group if all 5 show up)

5 subsets of 1 person (each individual person)

10 subsets of 2 people (all possible pairs from 5 people)

10 subsets of 3 people

5 subsets of 4 people

To summarize:

Subsets of size 1: 5

Subsets of size 2: 10

Subsets of size 3: 10

Subsets of size 4: 5

Subsets of size 5: 1

In total, there are 5 + 10 + 10 + 5 + 1 = 31 possible subsets of any size from a set of 5 people.

So if 5 people may show up and meet as 1 group, there are 31 total possible subsets of those 5 people.

User Anupsabraham
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