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Combination and Permutation Formulas:
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Combinations and permutations are fundamental concepts in combinatorics that deal with counting arrangements of objects. Combinations focus on selections where order doesn't matter, while permutations consider arrangements where order matters.
On a TI-84 calculator, you can calculate combinations and permutations using built-in functions:
Combinations: Press [MATH] → PRB → nCr
Permutations: Press [MATH] → PRB → nPr
Example: To calculate 5 choose 2 (5C2), enter: 5 [MATH] → PRB → nCr → 2 [ENTER]
Combinations: Order doesn't matter (e.g., selecting committee members)
Permutations: Order matters (e.g., arranging books on a shelf)
The key difference is whether the arrangement/order of selection is important in the context of the problem.
Tips: Enter the total number of items (n) and the number of items to select (r). Ensure r ≤ n and both values are non-negative integers.
Q1: When should I use combinations vs permutations?
A: Use combinations when order doesn't matter (selecting items), use permutations when order matters (arranging items).
Q2: What's the maximum value I can calculate?
A: The TI-84 can handle values up to n=69 for accurate factorial calculations due to floating-point precision limits.
Q3: Can I calculate combinations with repetition?
A: The standard nCr function doesn't handle combinations with repetition. Those require a different formula: C(n+r-1, r).
Q4: Why do I get an error when r > n?
A: Mathematically, you cannot choose more items than available. The calculator returns 0 for such cases.
Q5: Are there real-world applications of these calculations?
A: Yes! Used in probability, statistics, lottery calculations, password combinations, and many combinatorial problems.