Question 246478: Ok so: There are 15 questions on a multiple-choice exam and five possible answers to each question.
(a) In how many ways can the exam be answered? (I put 5^15 is that correct? Since the questions are all distinct, and any number of questions could be answered for example a out of a,b,c,d,e.)
(b) In how many ways can the exam be answered with exactly 8 answers correct? (Is this 5^7?)
Thanks
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! a-
There are 15 questions.
Each question has 5 possible answers.
5^15 is not correct.
Why are you trying to raise 5 to a power?
Think about what that does.
let's say there are only two questions with 5 possible answers
so with your method there would be 5*5 possible answers=25
but we know
the first question has 5 possible answers
the second questions has five possible answers
lets make it only three questions
the first question has 5 possible answers
the second questions has five possible answers
the third question has five possible answers
This should give you a hint to how many answers 15 questions might have.
b-
so what has happened?
8 questions have been reduced to only one possible answer -the correct one.
that leaves 7 with 5 possible answers
so work out how many possible answers there are for those 7 and add 8 to it for the 8 correct answers
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