Question

Question #87f7d

Answer 1

There are `2^10` (1024) ways the answers could be arranged.

Explanation:

There are ten questions, but each question can be answered in two ways.

To help you understand the process, let's start with fewer questions - only two.

After answering T or F on the first (two ways possible) you could also choose T or F on the second. So, the possible patterns are:

TT TF FT FF four ways (2 x 2) = `2^2`.

Increase to three questions, and each of these four possible patterns gives rise to two more possibilities:

TTT TTF TFT TFF FTT FTF FFT FFF

Now, we have eight ways (2 x 2 x 2) = `2^3`

Carry on in this way, and you will find that four a test with ten questions, you could answer in `2^10` ways.

(Because only one of these arrangements yields a perfect test score, your chances are pretty slim if you have to guess at every one!)

Answer 2

`2^10 = 1024` arrangements.

Explanation:

If we assume that the questions are numbered, then they will always be in that order.

Each question can be either 'True' or 'False' - so there are 2 options.

Therefore the number of arrangements of True and false is:

`2xx2xx2xx2xx2xx2xx2xx2xx2xx2 = 2^10`

`2^10 = 1024` arrangements.