(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

To win a lottery, must pick 5 different numbers from the 45 available.

The order in which the numbers are chosen does not matter.

With only one ticket, what is the probability of winning (i.e. matching all 5 numbers drawn with all 5 chosen) ?

2. Relevant equations

Stated within the solution

3. The attempt at a solution

n = number of elements in the field (in this case, 45)

p = number of choices (5)

[tex]P(win) = \left(\frac{n!}{(p!(n - p)!)}\right)[/tex]

Therefore:

[tex]=\left(\frac{45!}{(5!(45- 5)!)}\right)[/tex]

[tex]=\left(\frac{45!}{(5!)(40!)}\right)[/tex]

[tex]=\left(\frac{45!}{(120)(40!)}\right)[/tex]

[tex]=\left(\frac{45!}{(5!(40)!)}\right)[/tex]

[tex]= \left(\frac{45*44*43*42*41}{120}\right)[/tex]

[tex]=1221759[/tex]

Therefore:

[tex]P(win)= \left(\frac{1}{1221759}\right) \approx 8.18\times10^{-7}[/tex]

.. Is this correct method / answer?

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# Homework Help: Probability Calculation - Lottery

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