All Combinations of a set of songs?

Question

My country has a weekly song chart with 10 songs. There is another WATCH OUT list with another 10 songs. Always the chart will consist of 10 songs out of the mentioned 20. There is a gift pack on offer to anyone who predict the chart correctly.

Would any one know a easy way to get all the possible combinations with these 20 songs using excell or something? I think that there would be 10x10x10 entries.

I did find some small prgms that was to be run in excel - but none of them worked or I dont know how to run them in excel correctly

Can anyone out there help me?

Thanks,

thush

Answer 1

I suck at excel but mathematically, this is what you want to do: select 10 random songs from 20 available songs
Thats 20C10 combination and resolves to a total of 184756 ways of selection
It may not be easy for any software to list our that many options.
I remember writing a program to do that. It would take my program approx 2-3 minutes to list that many options maybe
But I dont think you are looking at that at all.. I think you are better of guessing here than trying to run any program.

Answer 2

What you have is 20 songs, and you want to know how many ways you can pick 10 songs.

From combinatorics, we call this 20 choose 10 = 20! / (10! * 10!) = 184756 combinations.

To list all those combinations, you need to write a computer program. Python would be a good language and you'll need to use recursion. Start with your set of 20, choose one, and recurse to add each element to the smaller set. Then count the output. This is about late 1st year, 2nd year computer science stuff.

Glad you asked?

Answer 3

If the order of the songs is important, there are about 6.7x10^11 combinations.

This is a permutation without repetition, so combinations equals 20!/10!. See the link for more detail.

If order doesn't matter, there are only 184756 combinations.