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A quiz has ten questions: 7 true/false and 3 multiple choice. the multiple choice...

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A quiz has ten questions: 7 true/false and 3 multiple choice. the multiple choice questions each have four options. How many ways can the test be answered?

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The quiz has ten questions of which 7 are true/false questions and 3 are multiple choice questions with each having four options.

When the test is answered each of the true/false questions can be answered in 2 ways. This allows them to be answered in 2^7 ways. The 3 multiple choice questions have 4 options and can be answered in 4^3 ways.

In all, there are 2^7*4^3 ways to answer the test.

2^7*4^3  = 128*64 = 8192

The test can be answered in 8192 ways.

 

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