Question

How many possible finishes are there for first, second, and third place in a marathon with
100 entries?

Answer 1

The first place winner can be any one of the runners, correct? How many possibilities are remaining for the second place finisher? (Note: we could start with any of the places first -- first place, second place, or third place, but I chose to start with the first place winner.)

Answer 2

99 is for the second place, and 98 for the third place?

Answer 3

It is an nPr (permutations)

100P3

Answer 4

if I may ask
how can you tell if its a permutation. I'm not the best at data lol

Answer 5

Dude, yup, so, it's 100 possibilities for first place, 99 for second, and 98 for third.

Answer 6

In total, how many possibilities are there? (hint: product of the possibilities)

Answer 7

Lets say your are asked the number of combinations on a computer password, then entering lets say
a34, is not the same as 3a4
the order matters

in combinations you are choosing lets say 10 players out of 40 students then the order doesn't matter, becuase, lets say
saying that Mark and John are on the team is same as saying that John and Mark are on the team.

Answer 8

Dude, you can tell if its a permutation if order matters.

Answer 9

there are 970,200 possibilities
and im doing this data assignment and im lost?

Answer 10

and thanks SoloMon. so, each question is either a combination or a permutation? and I just use one of the formulas to solve them?

Answer 11

So, for instance, three people -- Bob, Alice, and Frank -- are in a race. Bob getting first place, Alice second, and Frank third is different than Frank getting first, Alice getting second, and Bob getting third.

Answer 12

If order doesn't matter, e.g., how many ways can you choose who will be in the top three (and the order of first, second, and third doesn't matter), is not a permutation problem. That is a combination problem, i.e., (100 choose 3).

Answer 13

queelius, don't you agrre that what you said for the entire answer, is just a description of one possible combination ?

Answer 14

I understand now

Answer 15

What I said for the entire answer is all of the possible assignments of people to the top three places. One possible combination would just be a single such assignment.

Answer 16

wait what ?!?!?!

you have 100 people and you want to know in how many possible ways can these 3 places appear. SAo you are saying that the answer is 98*99*100 ?!

Answer 17

Yes.

Answer 18

@queelius , I am not good at math, but THIS I do know, and know for sure.
You can ask your teacher if you don't trust me.

Answer 19

What do you know? Are you disagreeing with the answer I provided? We can go over a simpler problem to reveal why my answer is correct if you wish.

Answer 20

Btw, when I said "what do you know" that was in response to your "but THIS I know". I did not mean it as an insult.

Answer 21

I don't understand that answer either but It does make sense that it is a combination

Answer 22

I am going to try my best right now, to explain why you are incorrect.

To make it simpler, lets say you have 10 runners and you are to list all possible ways of 1st 2nd and 3rd place . (lets call racers, A B C D E F G H I J )

So your first option would be
A, B, C, D, E, F, G, H, I, J
A, C, B, D, E, F, G, H, I, J

those 2 are different, it is not just permutations though that what my mistake is.

Answer 23

( the first 3 spouts are 1st 2nd and 3rd places )

Answer 24

First, the two lists you provided are permutations. But the key insight here is that we are only interested in selecting letters from {A, B, C, ..., J} for three positions, no repetitions allowed.

So, let's consider a simpler problem. Suppose we have three people, A, B, and C, and we want to know how many possible ways there are for the top 2 places. My answer, then, is simply 3 * 2.

A B
A C
B A
C A
B C
C B

Which is also 6 and exhaustive.

Answer 25

you actually going

100 C 3 (nCr function)
and then you would multiply it times (3 nCr 3), being that in each combination, you have (3 P 3), becuase there can be different orders among places.

So the answer is

100 nCr 3 times 3 NPr 3

Answer 26

I am not in the mood of giving an entire class about combinations and permutations right now... have a good one everyone in this question :)

Answer 27

My answer is (100 choose 3) * 3!, which is the same as 100*99*98, or 100!/(100-3)!. But, we don't have to use that, we can just think it through:

In the first place, we have 100 possible people we can assign to it. In the second place position, we have 99 possible people, Finally, in the third place, we have 98 possible people we can assign to it.

Answer 28

solomon, then whats the real answer for my question then?

Answer 29

hey queelius, I have other questions that I need help with, do u mind helping me?

Answer 30

Dude, ask away.

Answer 31

I said it, but no one wants to listen to me. I think I am better leave this question right now.

Answer 32

Solomon, what is your answer for my simpler example? I believe we may be able to clear any confusion either of us have by considering the simpler example.

Answer 33

your answer is the same as queelius, what are you guys even arguing about lol?

Answer 34

Dude, lol, I didn't even check his answer. It appears we may be arguing for no reason at all, then.

Answer 35

he said 100p3

Answer 36

which is basically the same as yours

Answer 37

Indeed. It's the exact same.

Answer 38

lol

Answer 39

I apologize for not looking over your answer more carefully, Solomon.

Answer 40

How many arrangements can be made from the letters in LILLEHAMMER if

Answer 41

the arrangement must start with an H and end with an M