# Permutation or Combination?

• Feb 23rd 2009, 08:33 PM
transformers2009
Permutation or Combination?
Don't solve these. Just specify whether they're Permutation or Combination.

1) If only 8 motorcycles can race at a time, how many different groups of competitors can be made up from 12 cyclists? My Answer: Combination - since it doesn't specify order of importance.

2) In how many ways can 12 motorcycles be lined up for a race? My Answer: Permutation - order will matter because we will arrange all motorcycles & want to find out all ways to order them.

3) The art director for a museum has eight paintings and only six spaces on the wall to hang paintings. How many ways can he arrange the eight paintings to fill the six spaces? My Answer: Combination - doesn't really specify the importance of order of paintings on the wall.

4) How many different groups of six paintings can be hung? My Answer: Permutation - order will matter because we need to track of the many ways a painting can be arranged.

5) How many possible ways could seven intramural baseball teams finish the season ranked according to their winning record?
Combination - it doesn't matter who is ranked; thus there's no specific order for teams to be ranked.

6) How many possible ways could two trophies (for champion team & runner-up team) be awarded if there are seven teams? Permutation - order matters because trophies are specified for ranking high.

Correct me where I'm wrong. Appreciate all the help I get from here. Again, I don't want answers to the problem: I would just like to see a Combination or Permutation labeled next to them (& if you can explain your answer that would help too). Thanks! Also, any tricks to better distinguish this comparison would be much appreciated.
• Feb 23rd 2009, 10:55 PM
Janu42
Quote:

Originally Posted by transformers2009
Don't solve these. Just specify whether they're Permutation or Combination.

1) If only 8 motorcycles can race at a time, how many different groups of competitors can be made up from 12 cyclists? My Answer: Combination - since it doesn't specify order of importance.

2) In how many ways can 12 motorcycles be lined up for a race? My Answer: Permutation - order will matter because we will arrange all motorcycles & want to find out all ways to order them.

3) The art director for a museum has eight paintings and only six spaces on the wall to hang paintings. How many ways can he arrange the eight paintings to fill the six spaces? My Answer: Combination - doesn't really specify the importance of order of paintings on the wall.

4) How many different groups of six paintings can be hung? My Answer: Permutation - order will matter because we need to track of the many ways a painting can be arranged.

5) How many possible ways could seven intramural baseball teams finish the season ranked according to their winning record?
Combination - it doesn't matter who is ranked; thus there's no specific order for teams to be ranked.

6) How many possible ways could two trophies (for champion team & runner-up team) be awarded if there are seven teams? Permutation - order matters because trophies are specified for ranking high.

Correct me where I'm wrong. Appreciate all the help I get from here. Again, I don't want answers to the problem: I would just like to see a Combination or Permutation labeled next to them (& if you can explain your answer that would help too). Thanks! Also, any tricks to better distinguish this comparison would be much appreciated.

It looks like your answers are right, except for #5 I think it may be a permutation. There's only 7 teams, so it's asking how many different ways can they finish in the standings (correct me if there's not just the 7 teams). So all the different ways they finish are different permutations.
• Feb 24th 2009, 12:24 AM
Greengoblin
I think you got 3 and 4 the wrong way round. whenever it uses the word "arrange" it implies that order matters, but whenever it talks about "how many groups" it implies order doesn't matter but only the combination does.
• Feb 24th 2009, 02:17 PM
Janu42
Quote:

Originally Posted by Greengoblin
I think you got 3 and 4 the wrong way round. whenever it uses the word "arrange" it implies that order matters, but whenever it talks about "how many groups" it implies order doesn't matter but only the combination does.

Yes, I agree with this as well. So 3, 4, and 5 are wrong I think in what you said originally.