Decide which of the scenarios below should be counted using permutations or combinations. Scenario I:
Number of ways 12 movies can be ordered to play on television.
Scenario II:
Number of ways three different roles can be filled by 11 people auditioning for a play.
Scenario III:
Number of different two-topping pizzas that can be made from an assortment of 10 different toppings.
A)Scenario III is a combination and scenarios I and II are permutations.
B)All scenarios are combinations.
C)Scenario II is a combination and scenarios I and III are permutations.
D)Scenarios I and II are combinations and scenario III is a permutation.
E)All scenarios are permutations.

Question

Quizplus · Accepted Answer

Scenario I involves the ordering of movies, which implies a specific arrangement, so it should be counted using permutations.

Scenario II involves filling specific roles, but the order in which the roles are filled is not important, so it should be counted using combinations.

Scenario III involves selecting toppings for a pizza, but the order in which the toppings are selected does not matter, so it should be counted using combinations. Therefore, only options A and C are possible, but since scenario II is a combination in all the options, the correct choice is A.

Decide Which of the Scenarios Below Should Be Counted Using