Math Problem Statement
How many unordered sets are there of four items chosen from eight? sets
Solution
To determine the number of unordered sets of four items chosen from a total of eight, we use the concept of combinations. For an unordered set (where the order of selection doesn't matter), the formula for combinations is:
where:
- (the total number of items),
- (the number of items to choose).
Plugging in the values:
Now, calculate each part:
-
, but since it divides by , we can simplify this to .
-
Calculating the above:
-
Now divide by :
So, there are 70 unordered sets of four items chosen from eight.
Would you like further details or have any questions?
Related Questions
- How would the answer change if we chose 5 items from 8 instead of 4?
- What if we chose ordered sets instead of unordered sets?
- How many unordered sets are there of three items chosen from eight?
- What is the total number of combinations if we choose two items from eight?
- How does this calculation change for a scenario with replacement?
Tip:
When solving combination problems, always simplify factorial expressions as much as possible before multiplying to make calculations easier.
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Math Problem Analysis
Mathematical Concepts
Combinatorics
Combinations
Formulas
Combination formula: C(n, r) = n! / [r! * (n - r)!]
Theorems
Basic counting principle in combinatorics
Suitable Grade Level
Grades 10-12