# Thread: Combinations/Permutations where only certain elements in series can vary

1. ## Combinations/Permutations where only certain elements in series can vary

Hi all,

I am sorry if this is posted the wrong sub-forum, but my math knowledge is limited and so I am unsure where else to post.

I am wondering how to calculate the number of possible versions of a series of characters, where only some characters in the series can vary.

5NMB RTTM 8L60 9P7U AJQW 9889

 5 N M B R T T M 8 L 6 0 9 P 7 U A J Q W 9 8 8 9 L N G O 4 3 V B B

How many different combinations are possible where only bold characters can vary and they can vary only with the character directly beneath them in the table? Is there a formula for this?

Therefore, the following are possible (characters in red are variations on the original series):

5NMB LTTM 8L60 9P4U AJQW 9889

5NMB RTTM 8L60 9P7U AJQW 9BB9

5NMB LTTN 8LGO 9P4U A3QV 9889

But the following is NOT:

5NMB NTTO 8L60 9P7U ABQB 93V9

I hope this makes sense, and I hope it is ok to post here. I am new to the forum so forgive me if my posting etiquette or anything is off-point.

I look forward to your responses.

2. If I understand the problem, you have a sequence of characters. At specific spots in the sequence, a character may be replaced by one other character.

You have 9 spots where an alternative is permitted.

So the number of possible different sequences is $2^9 = 512.$