Factorial, Permutation and Combination

How many different three-digit odd numbers can be formed using the digits in the set

{4, 5, 6, 7, 8, 9}?

• 6.6.6

• 6.5.4

• 6.6.3

• 6.5.3

How many three-digit counting numbers are there?

• 990

• 900

• 999

• 1000

Nicole has four different skirts, three different blouses and two pairs of shoes which she can wear for a business meeting. In how many ways can Nicole dress for the meeting?

• 9

• 12

• 18

• 24

Mary has three different Barbie dolls and two different Cindy dolls. She wants to take them out to play with her friend. However, Mary’s mother will only let Mary choose one doll. In how many ways can Mary choose a doll?

• 5

• 6

• 3

• 1

A briefcase has a five-digit combination lock. The second digit in the combination is 5. At most how many different combinations must we try if we want to open the lock?

• 1000

• 10000

• 100000

• 99999

A four-digit number is formed using the digits in the set {1, 2, 3, 4, 5, 6}. How many numbers can be formed if no digit can be used more than once?

• 6! = 720

• 6⁴ = 1296

• 6.5.4.3 = 360

A three-digit number is formed using the digits {0, 1, 2, 3, 4, 5}. How many different numbers can be formed?

• 6.6.6 = 216

• 6.5.4 = 120

• 5.6.6 = 180

• 5.4.3 = 60

A box contains 5 different white balls and 7 different red balls. In how many ways can we randomly pick a ball from the box?

• 2

• 1

• 12

• 35

What is the number of permutations of 5 different math books piled on a table?

• 5

• 25

• 4

• 5!

Aleks has 5 different math books, 3 different biology books and 4 different physics books. In how many different ways can Aleks arrange his books on a book shelf?

• 5!.3!.4!

• 12!

• 5.3.4

• 5 + 3 + 4