A quiz has 8 questions, each answered True or False.
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A quiz has questions, each answered True or False. In how many ways can the whole quiz be answered? In how many ways if a question may also be left blank?
Need a reminder? The key ideaShow
If one event can happen in ways and, after it, a second event in ways, the two together can happen in ways. With repetition, each place keeps all its choices; without repetition, each place has one choice fewer than the one before.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Two choices each. ways.
Step 2. Three choices each. True, False or blank: ways.
Answer: ways, and with blanks allowed. Only one of the is all correct, which is why guessing rarely pays.
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