A quiz consists of five truefalse questions and five multipl

A quiz consists of five true/false questions and five multiple choice questions each of which has four possible answers: a,b,c or d. How many different ways can this quiz be answered? The BU lottery has 10 white balls numbered 1 through 10 and 10 red balls numbered 1 through 10. If three balls are randomly chosen, and if color matters, how many possible outcomes are there for this lottery? As in the Illinois lottery, order is not important.

Solution

1.

There are 4*4*4*4*4 = 1024 ways to answer. [ANSWER, 1024]

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2.

As we can see, these are actually 20 unique balls.

So, you can choose 3 balls out of 20 regardless of order, so we use combinations.

Hence, there are

20C3 = 20!/(3!17!) = 1140 outcomes [ANSWER]