Question

A true false test has 15 questions. How many answer keys are possible of the answer to 6 of the questions is false and 9 are true?

I think this is a permutation and not a combination because each answer key would be different depending on the order of which are true or false.

I think the answer is 15P9 x 15P6

Am I right?

Answer 1

lets look at an example. A four q test, 3 t, 1 f

tttf
fttt
tftt
ttft

4!/1! * 4!/3!=4*3*2*4 Nope..
What about 4!/3!1!

lets try that then with a five q, 3T, 2F
tttff
ttftf
tfttf
ftttf
fttft
ftftt
ffttt
tfftt
ttfft
tftft
5!/3!2!=5*2=10 And ten it is.

Answer 2

Thanks for typing that all out! It really helped.