AMC Combinations and Permutations

In how many ways can the letters of the word MATH be arranged?

• 4

• 8

• 12

• 24

In a group of 2 cats, 3 dogs, and 10 pigs in how many ways can we choose a committee of 6 animals?

• 1001

• 5005

• 3003

• 4004

Consider the set of 5-digit positive integers. How many have at least one 7 in their decimal representation?

• 52488

• 52484

• 37512

• 45000

In how many ways can one book be selected from a bookshelf of 5 paperback books and 3 hardcover books?

• 5

• 3

• 8

• 11

How many ways are there to arrange 5 people in a row of 5 seats?

• 5

• 10

• 12

• 120

A girl has 5 shirts, 4 skirts and 3 pairs of shoes. How many different outfits can she create?

• 120

• 60

• 15

• 12

• 20

How many triples of three positive integers (x,y,z) have the product of 24?

• 20

• 24

• 27

• 30

In how many ways can 5 books be arranged on a shelf if two of the books must remain together, but maybe interchanged?

• 12

• 24

• 48

• 96

How many ways can 5 distinct paperback books and 1 hardcover book be arranged on a shelf if the hardcover must be the rightmost book on the shelf?

• 20

• 60

• 90

• 120

How many four-digit whole numbers do not contain the digit 1? No digit is allowed to be used more than once in any such 4-digit number.

• 4032

• 2016

• 2688

• 8064