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Combinations Formula:
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The combinations calculation (2^n) determines the total number of possible subsets that can be formed from a set of n distinct items. This includes all possible combinations from the empty set to the complete set.
The calculator uses the combinations formula:
Where:
Explanation: For each item in the set, there are 2 possibilities: either the item is included in a subset or not. With n items, the total number of possible combinations is 2 multiplied by itself n times.
Details: This calculation is fundamental in probability, statistics, computer science, and combinatorics. It helps determine possible outcomes, analyze algorithms, and solve counting problems.
Tips: Enter the number of distinct items (n) in the set. The calculator will compute 2^n, which represents all possible subsets including the empty set and the full set.
Q1: What's the difference between combinations and permutations?
A: Combinations consider subsets regardless of order, while permutations account for different orderings. This calculator counts all possible subsets (combinations).
Q2: Why does the empty set count as a combination?
A: The empty set is a valid subset that contains no elements. It's included in the total count of 2^n possible subsets.
Q3: What's the practical limit for n in this calculator?
A: The calculator accepts values up to n=100, but results for n>30 will be very large numbers (over 1 billion combinations).
Q4: How is this related to binary numbers?
A: Each combination corresponds to a unique binary number of length n, where each bit represents whether an item is included (1) or not (0).
Q5: Can this be used for probability calculations?
A: Yes, knowing the total number of possible combinations (2^n) is often the denominator in probability calculations involving subsets.