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# Really stuuupid maths question

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Hi guys, for some reason I cannot seem to work this out, when it the type of simple math I should be use to. The problem is have a grid of 10x3 units, each grid location can either be a zero or a one, what the total amount of combinations the grid can possibly have? Please help, I feel dumb thanks DarkStar UK ------------------------------- Loves cross-posting because it works

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(number of states per unit) to the power of (number of units)

So here the answer is 2^30

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These types of problems, usually, are easy to work out.. once you realize the "trick."

If you need to count the number of ways to "do" something, first break it into a series of steps, count the number of ways to do each step, and take the product of all ways to do each step. This works if the number of ways to do step N is constant, no matter how a preceeding step was performed.

In your example, consider breaking the operation of choosing a combination into 30 steps ..

Step 1: Choose a 1 or 0 for the first "slot", 2 ways to do this.
Step 2: Choose a 1 or 0 for the second "slot", 2 ways to do this.
Step 3: Choose a 1 or 0 for the third "slot, 2 ways to do this.
... (and so on)
Step 30: Choose a 1 or 0 for the thirtieth "slot", 2 ways to do this.

There''s 30 steps, because there''s 10 * 3 "slots". Each step can be done 2 ways, so take the product of all the steps: 2^30.

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