1. What is the Probability and Combination Formula?

The formula calculates the probability of selecting exactly k items from a set of n items, where each item has an equal probability of being selected or not selected.

2. How Does the Calculator Work?

The calculator uses the probability formula:

Where:

• \( P \) — Probability (dimensionless)
• \( C(n,k) \) — Number of combinations (dimensionless)
• \( n \) — Total number of items (dimensionless)
• \( k \) — Number of selected items (dimensionless)

Explanation: The formula calculates the ratio of favorable combinations to all possible outcomes.

3. Importance of Probability Calculation

Details: Probability calculations are fundamental in statistics, gambling theory, risk assessment, and many scientific fields.

4. Using the Calculator

Tips: Enter positive integers for n and k, with k ≤ n. The calculator will compute the number of combinations and the probability.

5. Frequently Asked Questions (FAQ)

Q1: What does C(n,k) represent?
A: C(n,k) is the binomial coefficient, representing the number of ways to choose k items from n without regard to order.

Q2: Why is the denominator 2^n?
A: 2^n represents all possible subsets of n items, where each item can be either included or excluded.

Q3: What's the range of possible probability values?
A: The probability ranges from 0 (impossible) to 1 (certain). For k > n, P = 0.

Q4: Can this calculator handle large values of n?
A: It can handle moderately large values, but extremely large n may cause computational limitations.

Q5: How is this different from binomial probability?
A: This is a special case of binomial probability where success and failure probabilities are equal (p = 0.5).