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Permutations and combinations — Combinations 28 problems

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📘 Notes

Combinations

A combination is a way of selecting objects where order does not matter.

1. Key Idea

Key words: chosen, selected.

Different orders represent the same selection.

2. Combination Formula

\[ ^nC_r=\frac{n!}{r!(n-r)!} \]

3. Example

How many ways can 3 students be chosen from 5 students?

\[ ^5C_3=\frac{5!}{3!2!} \] \[ =\frac{120}{6\times2}=10 \]
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