Permutations and Combinations

The ski club with ten members is to choose three officers: captain, co-captain, and secretary. How many ways can those positions be filled?

• 720

• 120

• 540

• 72

A company has 10 members on its board of directors. In how many different ways can it elect a president, vice-president, secretary and treasurer?

• 210

• 5040

• 1080

• 720

For a segment of a radio show, a DJ can play 4 songs. If there are 8 songs to select from, how many different ways can the program for this segment be arranged?

• 70

• 210

• 1680

• 1420

Suppose you are asked to list, in order of preference, the three best movies you have seen this year. If you saw 12 movies during the year, how many ways can the three best be chosen and ranked?

• 220

• 480

• 1560

• 1320

An election ballot asks voters to select three city commissioners from a group of six candidates. In how many ways can this be done?

• 20

• 120

• 540

• 180

A four-person committee is to be elected from an organization with 11 people. How many different committees are possible?

• 7920

• 330

• 4860

• 175

You are on your way to Hawaii and you want to bring some books on the plane. Of the 15 books in your collection, you can only fit 10 in your bag. How many different collections of 10 books are possible?

• 1.09x10¹⁰

• 5841

• 3003

• 2.41x10¹¹

In a race in which six automobiles are entered and there are not ties, how many different ways can the first four finishers come in?

• 360

• 15

• 240

• 30

A medical researcher needs 6 people to test the effectiveness of an experimental drug. If 13 people have volunteered for the test, how many different groups of 6 people can be formed?

• 1235520

• 1716

• 2078

• 100480

The special combo pizza at Ciro's Pizza includes any 5 toppings from the list of 16 toppings. How many different combo pizzas are possible?

• 524,160

• 15,870

• 6120

• 4368