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July 29th, 2017, 01:00 PM  #1 
Newbie Joined: Jan 2016 From: Ghana Posts: 17 Thanks: 4  Arranging numbers
Hi, So I'm faced with this problem: I want to form a 5 digit number such that 123 are always consecutive. Eg 51423 or 14253. 1,2 and 3 are always consecutive in these numbers How many of these numbers are possible. I tried doing it, but I always end up double counting. Furthermore, how will I expand it for forming a 6 digit number and so on? 
July 29th, 2017, 01:08 PM  #2 
Senior Member Joined: Oct 2009 Posts: 429 Thanks: 144 
Choose a place for 4, choose a place for 5. Then fill up the number with 123 in consecutvie order. So I choose place 1 for 4 to get 4**** I choose place 3 for 5 to get 4*5** I fill up the rest consecutively 41523 Does that tell you how many there are? 
July 29th, 2017, 01:17 PM  #3 
Newbie Joined: Jan 2016 From: Ghana Posts: 17 Thanks: 4 
I think I understand the process you are using to fill up the spaces. But how will I use that to get the total number of numbers.

July 29th, 2017, 02:37 PM  #4 
Global Moderator Joined: May 2007 Posts: 6,540 Thanks: 591 
There are 5 places for a 5. There are 4 places remaining for a 4. That's 20 setups. For each setup there is only one way to get 1,2,3 in order. Net result 20 combinations.


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