SOLUTION: In how many different ways can a true-false test consisting of 9 questions be answered?

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Question 1010835: In how many different ways can a true-false test consisting
of 9 questions be answered?



Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
In how many different ways can a true-false test consisting
of 9 questions be answered?

There are 2 ways to answer question 1.

For each of those 2 ways to answer question 1, 
there are 2 ways to answer question 2.
That's 2*2 or 22 ways to answer questions 1 and 2.

For each of those 22 ways to answer questions 1 and 2, 
there are 2 ways to answer question 3.
That's 2*2*2 or 23 ways to answer questions 1 through 3.

For each of those 23 ways to answer questions 1 through 3, 
there are 2 ways to answer question 4.
That's 2*2*2*2 or 24 ways to answer questions 1 through 4.

For each of those 24 ways to answer questions 1 through 4, 
there are 2 ways to answer question 5.
That's 2*2*2*2*2 or 25 ways to answer questions 1 through 5.

For each of those 25 ways to answer questions 1 through 5, 
there are 2 ways to answer question 6.
That's 2*2*2*2*2*2 or 26 ways to answer questions 1 through 6.

For each of those 26 ways to answer questions 1 through 6, 
there are 2 ways to answer question 7.
That's 2*2*2*2*2*2*2 or 27 ways to answer questions 1 through 7.

For each of those 27 ways to answer questions 1 through 7, 
there are 2 ways to answer question 8.
That's 2*2*2*2*2*2*2*2 or 28 ways to answer questions 1 through 8.

For each of those 28 ways to answer questions 1 through 8, 
there are 2 ways to answer question 9.
That's 2*2*2*2*2*2*2*2*2 or 29 ways to answer questions 1 through 9.

Answer: 29 = 512 ways.

Edwin
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