Question

Select all of the following situations that represent permutations rather than combinations. Choosing 5 people from a university program with 28 students to receive scholarships. Ways to line up the team along the blue line of a hockey rink prior to O Canada! Choosing an outfit consisting of tie, shirt, jacket, shoes, and trousers from a wardrobe with several of each. Taking the 10 best selling video games of the year and ranking them from best to worst. Matching 4 friends to 4 of the books you own. Parking 2 of 6 cars single file in a family's driveway when they are having a party. Choosing 1st, 2nd, and 3rd prize winners of a competition. Choosing 3 varieties of flowers from a selection of 15.

Answer 1

Permutations are used when order is important while a combination is used when we are only making selections.

a) Choosing 5 people from the program with 28 students is just choosing and not arranging in any order. Therefore this is a case of combination and not permutation

b) As we are lining up the team, therefore the order of people in line is important here ( that is person placed at front is different from placed at the back). Therefore the case here is of permutation.

c) As we are choosing the outfit here, and not arranging the chosen items, therefore this is not a case of permutation here.

d) As we are doing ranking also after selection of the best selling video games, therefore order is also important here. Therefore this is a case of permutation here.

e) As for each friend, we are giving a different book, therefore the total ways to do so is 4! which is a permutation. Therefore this is a case of permutation here.

f) As we are selecting 2 cars here from 6, this is a case of combination and not permutation

g) As each price is a distinct position here, therefore order is important here. Therefore this is a case of permutation here.

h) As we are only choosing the flowers and not arranging in any order, therefore this is not a case of permutation but a case of combination here.