So I have figured out this problem :So, for this week's forum we were given a problem to solve and explain how we got the answer. I must confess I was totally confused at first. I read and reread the entire chapter and then I look up more information on how to know which formula to use then it finally clicked. Permutations are for lists (order matters) and combinations are for groups (order doesn't matter).

So, for this problem:Suppose that a class contains 15 boys and 30 girls, and that 10 students are to be selected at random for a special assignment. Find the probability that exactly 3 boys will be selected.

I choose to use the combination rule:nCr = n!/(n-r)!r!

1). First, we should figure out the combinations involved in choosing 10 students out of 45 students:

45C10 = 45!/(45 - 10)!(10!) = 3190187286

2). Then the number of ways 3 boys can be chosen out of 15:

15C3 = 15!/(15-3)!(3!) = 455

3). Finally, the number of ways to choose 7 girls out of 30:

30C7 = 30!/(30-7)!(7!) = 2035800

4). Using the formula for Classical Probability, the number of outcomes in E is 455 * 2035800 = 926289000

5). Divide this number by the total number of outcomes in the sample space and round to two decimal places

926289000 / 3190187286 = 0.29035568

Answer: .2904 or 29.04% that three boys will be selected.

I am still not sure I have this chapter all figured out but it made me think about how to find the correct answer using the correct formula. Before this chapter I thought probability was based on chance or predictions. But to find out probability is the basis of inferential statistics. It is where predictions are based on probability and hypotheses are tested by using probability.

My question is: How do I explain how I can verify if the solution is correct or not?