1. Fundamental Principle of Counting
If one operation can be done in m ways, and a second independent operation can be done in n ways, then the total number of ways both can be done is m × n.
2. Permutations vs Combinations
- Permutation: Arrangement of objects where order matters (e.g., arranging books on a shelf). Formula:
nPr = n! / (n-r)! - Combination: Selection of objects where order does NOT matter (e.g., choosing a committee). Formula:
nCr = n! / [r! × (n-r)!]
3. Use in Probability
Combinations and permutations form the backbone of calculating sample spaces for complex probability problems, such as drawing hands of cards or lottery odds.
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