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How many possible song combinations can a user-formatted online radio station play if it has 1471 songs and randomly selects 10 songs to auto play at each visit to the page?
Darren1965
If the ordering of the 10 songs counts (e.g., a,b,c is counted as a different combination from b,c,a) then the number is
1471 * 1470 * ... * 1462 = 4.6005774 * 10^31
If the ordering of each set of 10 songs is not counted, then the number of combinations is the above number divided by 10!, which is 1.267796 * 10^25.
In general, the number of different ways to choose n things out of N objects where order does not matter is: N! / [n! * (N-n)!)]. If n were larger, such as choosing 500 songs out of 1471, you would have to use Sterling's approximation.
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