# Question #87f7d

Apr 15, 2017

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.

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!)

Apr 15, 2017

${2}^{10} = 1024$ 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:

$2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = {2}^{10}$

${2}^{10} = 1024$ arrangements.