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Probability with combinations

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Learn it When all outcomes are equally likely, probability = favourable ÷ total. Use combinations $C(n, r)$ to count groups where order doesn't matter.

Example: A committee of 3 from 4 girls and 5 boys. P(exactly 2 girls)?

  1. Total: $C(9, 3) = 84$.
  2. Favourable: $C(4, 2) \times C(5, 1) = 6 \times 5 = 30$.
  3. $\frac{30}{84} = \frac{5}{14}$.

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