Counting Rules

A combination is an ordered arrangement of objects.

• True

• False

The number of different ordered arrangements of n distinct objects is n!.

• True

• False

The number of ways 15 people can line up in a row for concert tickets.

• 1.31 x 10¹²

• 1

• 4.38 x 10¹⁷

• 15

The number of ways a 4-member committee can be chosen from 10 people.

• 3,628,800

• 10,000

• 5040

• 210

The access code for a car's security system consists of four digits. The first digit cannot be zero and the last digit must be odd. How many different codes are available?

• 10,000

• 6561

• 4500

• 5040

A horse race has eight entries. Assuming that there are no ties, in how may different orders can the horses finish?

• 40,320

• 1

• 8

• 16,777,216

The starting lineup for a softball team consists of 10 players. How many different batting orders are possible using the starting lineup?

• 3,628,800

• 10,000,000,000

• 1

• 10

A horse has 12 entries. Assuming that there are no ties, in how many different ways can these horses finish first, second, and third?

• 1728

• 1320

• 220

• 12

From a pool of 14 candidates, the offices of president, vice-president, secretary, and treasurer will be filled. In how many different ways can the offices be filled?

• 38,416

• 24,024

• 1001

• 14

From a group of 40 people, a jury of 12 people is selected. In how many different ways can a jury of 12 people be selected?

• 5,586,853,480

• 1.68 x 10¹⁹

• 2.68 x 10¹⁸

• 480