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July 25th, 2013, 01:09 PM   #1
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Total number of combinations

Hello everyone

I want to calculate how many combinations are there using 10 slots where:

3 slots can take 6 symbols
7 slots can take 10 symbols
There must always be 3 and 7 discrete slots.

For example 124F3DC587, where the capital letters can be A B C D E F and the numbers 0 1 2 3 4 5 6 7 8 9.

The clutch part is that I want only 3 slots containing 1 out of 6 symbols.

I can't figure out how to calculate this.
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July 25th, 2013, 07:18 PM   #2
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Re: Total number of combinations

Hello, crone!

Quote:
I want to calculate how many combinations are there using 10 slots where:,
[color=beige]. . [/color]3 slots can take 6 symbols,
[color=beige]. . [/color]7 slots can take 10 symbols.

For example: 124F3DC587,
[color=beige]. . [/color]where the letters can be {A,B,C,D,E,F} and the digits {0,1,2,3,4,5,6,7,8,9}.

From your example, I will assume that there are no "repeats".










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July 26th, 2013, 11:08 AM   #3
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Re: Total number of combinations

Hello!

Thanks for the reply, I actually do care about the repeats, forgot to mention it. But following your thinking proccess the total number of combinations should now be

. Which is actually the cartesian product of their respective combination tables (10^7 and 6^3 that is). I feel pretty stupid that I didn't think of that!
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July 26th, 2013, 11:11 AM   #4
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Re: Total number of combinations

Or is it



Sorry for double post but I cannot seem to find an edit button
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July 26th, 2013, 12:27 PM   #5
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Re: Total number of combinations

Hello again, crone!

Quote:
I want to calculate how many combinations are there using 10 slots where:,
[color=beige]. . [/color]3 slots can take 6 symbols,
[color=beige]. . [/color]7 slots can take 10 symbols.

For example: 124F3DC587,
[color=beige]. . [/color]where the letters can be {A,B,C,D,E,F} and the digits {0,1,2,3,4,5,6,7,8,9},
[color=beige]. . [/color]and "repeats" are allowed.












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July 26th, 2013, 01:01 PM   #6
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Re: Total number of combinations

Yea that's so much :O.

Thank you soroban you've helped me a lot!
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