Math Question - Possible combinations

Ritchmeister

Hey, i'm trying to figure out how many possible combinations there are to this question. I'm not neccesarily asking for the answer, but just a formula to help me figure out myself please.

If theres 15 questions in a test, each with 3 possible answers, how many possible combinations of answers is there altogether?

I have a feeling this could well be pretty simple, but I just suck at maths questions.

ecco the dolphin

Try looking at it like this:

If there is only 1 question in a test, with 3 possible answers, how many possible combinations are there?

3 combinations

If there are 2 questions in a test, with 3 possible answers, how many combinations are there?

We can count this - say the answers are labeled A, B, and C : AA, AB, AC, BA, BB, BC, CA, CB, CC. So 9.

So if there are 3 questions in a test, with 3 possible answers per question, how many combinations are there?

Count again: AA A, AA B, AA C, AB A, AB B, AB C, .... CC A , CC B, CC C. There'll be 27.

Can you see a pattern forming?

Movitz

[Edit] Sorry. I just went for the answer. eecc actually tried to explain.

Spoilered for people who likes thinkmaking by themselves

3*3*3*3*3*3*3*3*3*3*3*3*3*3*3=3^15=14348907

Ritchmeister

Well cheers, problem solved I guess.