Number of potential combinations

Question

Suppose we have a card which is used as a security device. This grid is always the same for a particular person and is a 10 x 7. Each cell of this grid contains two random letters or numbers 0-9 Ex. col 1 row 1 = "QW". The password generated from this is 6 letters long or made from 3 cells. I want to know how many possible combinations there could be of this.

My math/thinking as I am not a mathematician.

For one cell is 2 * 36 as there are two characters.

The grid is 10 x 7 so 70

70 * (2*36) = 5040

Now if the my previous math is wrong or not I am unsure how to calculate the repeat properly. I'm assuming it would be 5040 x 3 for the 6 length password?

Hello and welcome to math.SE. You are encouraged to learn MathJax typesetting on this site. It is likely to increase the quality of responses. — mathreadler, Oct 18 '17 at 20:34

Vasili · Accepted Answer · 2017-10-18T20:08:44.533

1

There are $26 \cdot 26$ combinations of two letters (26 ways to pick first letter and 26 ways to pick the second one). Then there are $70 \cdot 69 \cdot 68$ ways to pick three cells (after we pick the first cell we have 69 left, etc.) so the total number is 222025440. I assume that the position of the cell is important, i.e. the same 6-letter password but combined of different cells is a different password. Also, if you add numbers, there will be 36 ways to pick the first character.

edited Oct 18 '17 at 20:08

answered Oct 18 '17 at 20:00

Vasili

10,690

thank you for explaining, what is it mathematically called when you multiple by a number than a number - 1 like you showed above? – I'm here for Winter Hats Oct 18 '17 at 20:10
not quite sure what you are referring to (26 times 26 is "26 in the power of two"), the product of consecutive numbers from 1 to n is called a "factorial" – Vasili Oct 18 '17 at 20:17
Yeah I was looking for factorial, thanks – I'm here for Winter Hats Oct 18 '17 at 20:21

Number of potential combinations

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