Math Problem Statement
List all subsets of set A = {a, b, c, d} that have 3 elements.
Solution
To list all subsets of the set that have 3 elements, we need to select 3 elements out of the 4 available elements in the set.
The number of ways to choose 3 elements from a set of 4 is given by the binomial coefficient . This is equal to 4, which means there are 4 subsets of 3 elements.
The subsets of that have exactly 3 elements are:
These are all the possible subsets of size 3 from the set .
Would you like any further explanation or examples?
Here are some related questions:
- How do you calculate the number of subsets of a set of any size?
- How do you calculate the number of subsets of size from a set of elements?
- What is the difference between a subset and a proper subset?
- How can you list all subsets of a set with more elements?
- How do you determine the power set of a set?
Tip: To find subsets of a set, think of each element as either being in or out of the subset. This gives you a systematic way to generate all subsets.
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Math Problem Analysis
Mathematical Concepts
Combinatorics
Set Theory
Binomial Coefficients
Formulas
Binomial Coefficient \( \binom{n}{k} = \frac{n!}{k!(n-k)!} \)
Theorems
Combinatorial subset selection
Suitable Grade Level
Grades 7-10