Somebody solve it, by use combination like 5C3/(1/2)^5
That should be 5C3 / 2^5.
here the position is important.
Yes, it is. Do you know what that "5C3" means?
Let's use H for "Heads." Let's use T for "Tails". Every result of five tosses can be written to look like something this: HTTHH. (Here you first get heads, then 2 tails, then 2 more heads.)
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 1 2 33 4 5
Another way to think about it, is that we are choosing different places for the H's. If we choose places 1, 4 & 5, then we get HTTHH. If we choose places 2, 3 & 4, then we get THHHT. The heads are in different positions, which is important.
Every choice of three numbers (like the combination 1, 4 & 5) gives you a different result (like HTTHH). You can choose 3 numbers from 5 numbers in 5C3 different ways. Therefore, you have 5C3 different possible ways to get 3 H's in 5 tosses.
I'm so confused, the we use conbination if the position of heads and tails are not important.
No, that's not correct.
The order of the heads and tails matters
Here is what doesn't matter: it doesn't matter what order you put the three numbers in
. So if you put the heads in places 1, 4 & 5; that is the same as putting them in places 1, 5 & 4. Either way you get HTTHH.