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The fundamental counting principle states that if task 1 has m outcomes and task 2 has n outcomes, the sequential process has m × n outcomes. When multiple independent tasks are performed in sequence, total outcomes multiply.
Permutations (order matters): P(n, k) = n! / (n - k)!. Combinations (order does NOT matter): C(n, k) = n! / (k! (n - k)!). For example, selecting a committee of 3 from 8 people uses C(8, 3) = (8 × 7 * 6) / (3 × 2 * 1) = 56.
Worked example
1.Combinations C(n, k) are used when the selection order does not matter.
2.The value of C(5, 2) is equal to 20.
3.The number of distinct arrangements of 4 different books on a shelf is 24.
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