Combinatorics

[Kuja]

The question is as followed:

In how many ways can a student answer a true-false test that has six questions?

I tried nCr where n = 6 and r = 2
The result was 15, but at the back of the book it says 64!
I am wondering where the number 64 come from.

Thanks in advance!

[cookiemonster]

Each question is independent of each other. Each has two choices, so,

(choices for the first question)*(choices for the second question)*(choices for the third question)*(choices for the fourth question)*(choices for the fifth question)*(choices for the sixth question) = 2*2*2*2*2*2 = 2^6 = 64

I'm really not sure why you'd use 6C2.

cookiemonster

[Kuja]

O thank you!
I don't know, but I just don't understand the concepts.
I think I will read more.

[HallsofIvy]

Very good idea. But don' JUST read more. Before reading each example, try to solve it yourself. After you've done that, read the explanation of the example, then put the book aside and try to solve it yourself AGAIN. If you are a really good math student, the fourth or fifth time over each example, you will start to get it!