My Math Forum Total number of combinations

 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:
 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".

$\text{First, select the 3 slots for the letters.}
\;\;\;\text{There are: }\,_{10}C_3 \:=\:\frac{10!}{3!\,7!} \:=\: 120\text{ ways.}$

$\text{Then insert the 3 letters: }\:_6P_3 \:=\:\frac{6!}{3!} \:=\: 120\text{ ways.}$

$\text{Then insert the 7 digits: }\:_{10}P_7 \:=\:\frac{10!}{3!} \:=\:604,800\text{ ways.}$

$\text{Therefore, there are: }\:120\,\cdot\,120\,\cdot\,604,800 \:=\:8,709,120,000\text{ combinations.}$

 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 $10^7*6^3=2,160,000,000$. 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 $120*10^7*6^3$ 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:
 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.

$\text{First, select the 3 slots for the letters.}
\;\;\;\text{There are: }\,_{10}C_3 \:=\:\frac{10!}{3!\,7!} \:=\: 120\text{ ways.}$

$\text{Then insert the 3 letters: }\: 6^3\:=\:216\text{ ways.}$

$\text{Then insert the 7 digits: }\:10^7 \:=\:=\:10,000,000\text{ ways.}$

$\text{Therefore, there are: }\:120\,\cdot\,216\,\cdot\,10,000,000\:=\:259,200, 000,000\text{ combinations.}$

 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!

 Tags combinations, number, total

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Business Man Algebra 7 October 24th, 2013 06:19 PM AamirAli Algebra 5 March 4th, 2013 01:39 AM muhammadmasood Computer Science 7 September 14th, 2012 01:03 PM jsonliu Algebra 3 May 18th, 2010 05:01 PM Kenzo Algebra 14 August 13th, 2009 12:29 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top