Number of combinations with a grid and alphabet

Asked Sep 05 '16 at 21:22

Active Sep 05 '16 at 21:26

Viewed 114 times

Sorry, my previous question got deleted.

If I have a grid $N \times M$, and an alphabet of $S$ characters which can populate the grid, how many possibilities are there?

So if I had a $1\times 3$ and my alphabet was $\{A\}$, I would only have $\{A,A,A\}$, but if I had the alphabet $\{A,B\}$ I could have $\{A,A,A\}, \{B,B,B\}, \{A,B,B\}, \{B,A,A\}, \{A,A,B\}$, $\{B,B,A\}, \{A,B,A\}$, and $\{B,A,B\}$.

The answer given in my deleted question was $N\times M\times S$, but I don't think this is correct.

Is it $S ^{N\times M}$?

edited Sep 05 '16 at 21:26

Brian M. Scott

616,228

asked Sep 05 '16 at 21:22

user997112

2

Yes, it’s $S^{NM}$: you’re making an $S$-way choice $NM$ independent times. – Brian M. Scott Sep 05 '16 at 21:24
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You asked a similar question 5 minutes ago which I answered, then you deleted your post. At least I assume it was you. Edit: Ah sorry I didn't read the first line =) – ZirconCode Sep 05 '16 at 21:25
1

Yes indeed, you are correct =) – ZirconCode Sep 05 '16 at 21:29

Number of combinations with a grid and alphabet

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