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) =
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) =
Carry on in this way, and you will find that four a test with ten questions, you could answer in
(Because only one of these arrangements yields a perfect test score, your chances are pretty slim if you have to guess at every one!)
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: