Question

10. Determine whether the question can be answered using permutations or combinations.Explain your choice then answer the question. (3 points each)a.On a sailboat there are 6 signal flags. The order the flags are strung on the mastdetermines the signal being sent. How many 3-flag signals can the captain send?b. You are taking an online geometry quiz in which 6 questions are randomly selected froma test bank of 50 questions. How many versions of the quiz are possible?

Answer 1

a.

The question can be answered using the permutations because the order of the flag strung on the mast determines the signal being sent.

Since there are 6 signal flags and the captain has to send a 3-signal flag. So, the number of signals that can be sent are:

`\begin{gathered} _6P_3=(6!)/(\left(6-3\right)!) \\ =\frac{6*5*4*3!{}}{3!} \\ =6*5*4 \\ =120 \end{gathered}`

Thus, the answer is 120.

b.

The question can be answered using the combination because the questions are randomly selected.

Since the total number of questions is 50 and the number of questions that have to be selected is 50.

So, the number of versions of the quiz that are possible are:

`\begin{gathered} _(50)C_6=(50!)/(\left(50-6\right)!6!) \\ =(50*49*48*47*46*45*44!)/(44!6!) \\ =(50*49*48*47*46*45)/(6*5*4*3*2*1) \\ =(11441304000)/(720) \\ =15890700 \end{gathered}`

Thus, the answer is 15890700.