Example — Five-number win at the lottery

Example — Lottery, winning five-number combination

What is the probability of guessing a five-number combination at the lottery, choosing $5$ numbers out of $90$?

The total cases are the simple combinations of $90$ taken $5$ at a time (order does not matter):

$\binom{90}{5} = \frac{90\cdot 89\cdot 88\cdot 87\cdot 86}{5!} = 43\,949\,268.$

The favourable cases are $1$ (the winning five-number combination). So

$P = \frac{1}{43\,949\,268} \approx 2,3\cdot 10^{-8},$

roughly one chance in $44$ million.

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Topics: Probability
Concepts: Simple combinations · Probability
Methods: Simple combinations
Skills: Combinatorics · Probability calculation