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Counting and arrangements (contest style)
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Learn it Multiply the number of choices at each step (orders). If order doesn't matter, divide by the number of ways to arrange each group.
Example: How many ways can 3 class leaders be chosen from 6 students?
- In order: $6 \times 5 \times 4 = 120$.
- Each group of 3 can be ordered $3 \times 2 \times 1 = 6$ ways.
- $120 \div 6 = 20$ groups.
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