SOLUTION: Suppose a teacher gives a four question true-false test. The correct answers are F,T,T,F. If a students guesses the answers, how many of the outcomes would have exactly two corre

Algebra ->  Permutations -> SOLUTION: Suppose a teacher gives a four question true-false test. The correct answers are F,T,T,F. If a students guesses the answers, how many of the outcomes would have exactly two corre      Log On


   

Question 887675: Suppose a teacher gives a four question true-false test. The correct answers are F,T,T,F. If a students guesses the answers, how many of the outcomes would have exactly two correct answers?
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
It doesn't matter what the correct answers are.
We can choose 2 correct answers out of 4 in C(4,2)
ways. That's 4%21%2F%282%21%284-2%29%21%29 = 24%2F%282%2A2%29 = 6 ways.

You can check by listing them all and see that 6 is correct!

F, T, T, F
----------
T, T, T, T  2 correct  <--1 
T, T, T, F  3 correct
T, T, F, T  1 correct
T, T, F, F  2 correct  <--2
T, F, T, T  1 correct
T, F, T, F  2 correct  <--3
T, F, F, T  0 correct
T, F, F, F  1 correct
F, T, T, T  3 correct
F, T, T, F  4 correct
F, T, F, T  2 correct  <--4
F, T, F, F  3 correct
F, F, T, T  2 correct  <--5
F, F, T, F  3 correct
F, F, F, T  1 correct
F, F, F, F  2 correct  <--6

Edwin