Algebra: Counting principle and permutations

label Algebra
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A quiz has 4 multiple choice questions. If each has 5 choices, how many outcomes are possible?

May 6th, 2015

If there was only one question then there would be 5 outcomes - A,B,C,D,E


If the quiz had 2 questions then the outcomes would be - 

AA, AB, AC, AD, AE,

BA, BB, BC, BD, BE,

CA, CB, CC, CD, CE,

DA, DB, DC, DD, DE,

EA, EB, EC, ED, EE 

So there are 5*5 = 5^2 = 25 possible outcomes.


So continuing like this if the quiz had n questions with 5 choices for each question, the the number of possible outcomes would be 5^n.


So for a quiz with 4 questions, the number of possible outcomes = 5^4 = 625



May 6th, 2015

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May 6th, 2015
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