@Directrix
You're always really helpful, =) could you please help me with this problem?

Thirteen people are entered in a race. If there are no ties, in how many ways can the first three places be awarded?
a. 1716
b. 858
c. 39
d. 1684

Question

@Directrix 
You're always really helpful, =) could you please help me with this problem?

Thirteen people are entered in a race. If there are no ties, in how many ways can the first three places be awarded?
a. 1716
b. 858
c.  39
d. 1684

directrix · Answer

Order matters because there are lst, 2nd, and 3rd place awards.

@bumblebee3  How many different people could possible win lst place?

Please post that and then we'll do 2nd place.

anonymous · Answer

Okay, 13 different people could win 1st place. : )

directrix · Answer

Yes. One of them wins. 
Next question: How many different people are left for contenders for 2nd place?
Post and we'll do 3rd place and then put the problem together for a final answer.

anonymous · Answer

12 different people can get 2nd place.

anonymous · Answer

And 11 different people could get 3rd place. : )

directrix · Answer

Okay. Using the Fundamental (Basic) counting Principle as given on the attachment, there are 13*12*11 ways for 3 of 13 people to win lst, 2nd, and 3rd places. So what does that multiply out to be. @bumblebee3 And, you can study a bit more about the counting principle here: http://www.mathsisfun.com/data/basic-counting-principle.html

anonymous · Answer

Okay, so I got 13*12*11= 1716. Thanks for the website link!

directrix · Answer

1716 is what I got.

anonymous · Answer

Great! Thank you so much! =)

anonymous · Answer

Also, for this problem, I have a quick question! Does order matter? Because if it does, then the answer is 42, if it doesn't matter then the answer is 21. Thank you so much!
  A committee is to consist of two members. If there are seven people available to serve on the committee, how many different committees can be formed?

directrix · Answer

If you're on the committee, you are on the committee. Order does not matter.

Think about it this way: I'm choosing two people out of seven to give a free iDevice. Does it matter whether a person is chosen first or second? No, because both would get the gift.

So, run the combination formula through C(7,2) --> Seven, choose two.

anonymous · Answer

Alright, thank you so much for all your help! =)

directrix · Answer

You are welcome. P.S. I got 21.