Permutation or Combination?

Question

Read each of the following situations in order to determine if it is a permutation or a combination. Then, follow the instructions.

Situation A: Selecting a committee of 8 from a group of 35 students.

Situation B: Selecting who goes first, second, and third for oral reports in history class.

Situation C: Deciding which 4 runners will run the first, second, third, and fourth laps in a 4x400 relay.

Situation D: Selecting 3 toppings from a menu for a pizza.

Answer 1

Situation A is a combination because the order in which people are picked does not matter. There is no indication that the order in which the students are picked matters. A committee composed of Sally, Sue, Sam, Scot, Tom, Tina, Tracy, and Todd is no different from one composed of Sue, Todd, Sam, Tina, Sally, Tom, Scot, and Tracy.

Situation B is a permutation since it clearly draws a distinction between the three spots, indicating that order does matter. Tom, Sally, and Todd is different than Sally, Todd, and Tom.

Situation C is also a permutation for the same reason as Situation B. These are sometimes tricky, however, as they can be poorly worded. If the question read, "Deciding which 4 runners will run in a 4x400 relay," it might be harder to choose. Someone who is familiar with track events would know that it matters which runner runs which leg of the race, and might therefore deem it to be a permutation, however, the wording of the question doesn't make it clear that order matters.

Situation D is a combination because it doesn't matter which order the ingredients go on the pizza.