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
