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.