Math; Mixed Review of Outcomes

If 11 runners are participating a race, how many ways can there be first and second place runners?

110

How many different groups of three kids can you make from seven kids?

35

Which is greater 4P3 or 4C3?

4P3

In how many different ways can seven children line up in one row to have their picture taken?

5,040

permutations

arrangements of objects in which order is not important

There are 100 runners entered in a marathon. How many different groups of three runners can finish in first, second, and third? Does this problem involve permutations or combinations?

combination

element

one of the objects in a set

Do you use a mathematical permutation or a mathematical combination to open a combination lock?

permutation

There are 100 runners entered in a marathon. Trophies are awarded for first place, second place, and third place. In how many different ways could the runners receive trophies? Does this problem involve permutations or combinations?

permutation

combination

selection of objects where order is not important