Example · High school
Terms
| Term | This example | Why |
|---|
| binomial coefficient |
$\binom{49}{6} = 13\,983\,816$
|
Drawing $6$ lottery numbers from $49$ has
\[\binom{49}{6} = \frac{49 \cdot 48 \cdot 47 \cdot 46 \cdot 45 \cdot 44}{6!} = 13\,983\,816\]
outcomes, so a single ticket wins with probability about $1$ in $14$ million.
|
| combination |
✓ |
Each draw of $6$ lottery numbers from $49$ is a combination of $6$ of the numbers, because only the set of numbers drawn matters.
|
| permutation |
✗ |
A draw of $6$ lottery numbers from $49$ is not a permutation, because a ticket wins with the right numbers in every order of drawing.
|
Distinctions using this example
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