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July 25th, 2013, 01:09 PM  #1 
Newbie Joined: Jul 2013 Posts: 4 Thanks: 0  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. 
July 25th, 2013, 07:18 PM  #2  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Re: Total number of combinations Hello, crone! Quote:
From your example, I will assume that there are no "repeats".  
July 26th, 2013, 11:08 AM  #3 
Newbie Joined: Jul 2013 Posts: 4 Thanks: 0  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! 
July 26th, 2013, 11:11 AM  #4 
Newbie Joined: Jul 2013 Posts: 4 Thanks: 0  Re: Total number of combinations
Or is it Sorry for double post but I cannot seem to find an edit button 
July 26th, 2013, 12:27 PM  #5  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Re: Total number of combinations Hello again, crone! Quote:
 
July 26th, 2013, 01:01 PM  #6 
Newbie Joined: Jul 2013 Posts: 4 Thanks: 0  Re: Total number of combinations
Yea that's so much :O. Thank you soroban you've helped me a lot! 

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