# How many ways are there to answer a 20-question exam where 15 questions are true-false and 5 are MCQs with 4 choices?

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How many ways are there to answer a 20-question exam where 15 questions are true-false and 5 questions are multiple choice with 4 choices each?

posted Oct 26, 2018
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## 1 Answer

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To answer the first 15 questions with true or false there are 2^15 ways
And for the remaining 5 MCQs with 4 choices each there are 4^5 = 2^10 ways to answer them.
So there are 2^15 × 2^10 = 2^25 (33,554,432) ways to answer the exam. This means
Acing the exam by sheer chance is 1/2^25 = 1/33,554,432 =2.98023224 × 10^(-8) ie., very slim.

answer Oct 26, 2018

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