If a problem were asked, for example:
10 coins are flipped. What is the probability that 10 are heads?
Naturally, I would say, the probability of one coin being heads is .5, so, the probably of 8 coins being heads would be .5 * .5 * .5 * .5 * .5 * .5 * .5 * .5 or .5^8.
That's just what makes sense to me, and equals .0039.
However, the book goes about this question a very strange way. In my chapter on Binomial distribution, it uses combinations and says:
10 C 8 * (.5)^8 * (.5)^2
This method yields .043, which is supposedly the correct answer. These two methods are different and their answers are different. This entire chapter on binomial distribution is very bizare to me and makes no logical sense to me.
If anybody can help me understand why on earth this makes sense, I would appreciate it.