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

Solution:

Given, 9 questions are answered.

We have to find the different ways a true-false test consisting of 9 questions can be answered.

There are many ways to enumerate the combinations. The power set is the number of subsets of a set of n elements and it is given by 2ⁿ.

There are 2 ways to answer question 1.

Similarly, there are 2 ways to answer question 2.

i.e. 2² = 4 ways

For question 3 = 2³ = 8 ways

For question 4 = 2⁴ = 16 ways

For question 5 = 2⁵ = 32 ways

For question 6 = 2⁶ = 64 ways

For question 7 = 2⁷ = 128 ways

For question 8 = 2⁸ = 256 ways

So, for 9th question = 2⁹ = 512 ways

Therefore, there are 512 ways to answer 9 true-false tests.

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

Summary:

A true-false test consisting of 9 questions can be answered in 512 ways.