Fundamental Principles of Counting

In how many ways can the first five letters of the alphabet be arranged if each letter is used only once?

• 5 x 4 x 3 x 2 x 1 = 120

• 5 x 5 x 5 x 5 x 5 = 3125

• 26 x 26 x 26 x 26 x 26 = 11881376

• 5 + 5 + 5 + 5 + 5 = 25

In how many different ways can 4 different books be arranged on the shelf?

• 4 x 3 x 2 x 1 = 24

• 4 x 4 x 4 x 4 = 256

• 4 + 3 + 2 + 1 = 10

• 4 + 4 + 4 + 4 = 16

Marissa brought 8 T-shirts and 6 pairs of shorts to summer camp. How many different outfits consisting of a T-shirt and a pair of shorts does she have?

• 8 x 6 = 48

• 8 + 6 = 14

In a word-building game each player picks 7 letter tiles. If Julio's letters are all different, how many 3-letter combinations can he make out of his 7 letters?

• 7 x 6 x 5 = 210

• 7 x 7 x 7 = 343

• 3 x 3 x 3 = 27

• 3 x 2 x 1 = 6

The editor has accepted six articles for the newsletter. In how many ways can the six articles be ordered?

• 6 x 5 x 4 x 3 x 2 x 1 = 720

• 6 x 6 x 6 x 6 x 6 x 6 = 46656

• 6 x 6 = 36

There are ten one-hour workshops scheduled for the open house at the greenhouse. There is only one conference room available. In how many ways can the workshops be ordered?

• 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3628800

• 10 x 1 = 10

• 10¹⁰ = 10000000000

There are 6 different packages available for school pictures. The studio offers 5 different backgrounds and 2 different finishes. How many different options are available?

• 6 x 5 x 2 = 60

• 5 x 2 = 10

• 6 + 5 + 2 = 13

How many 5-digit even numbers can be formed using the digits 4, 6, 7, 2, 8 if digits can be repeated?

• 5 x 5 x 5 x 5 x 4 = 2500

• 5 x 5 x 5 x 5 x 5 = 3125

• 5 x 4 x 3 x 2 x 1 = 120

How many 4-digit positive even integers are there?

• 9 x 10 x 10 x 5 = 4500

• 10 x 10 x 10 x 10 = 10000

• 10 x 10 x 10 x 5 = 5000

• 5 x 5 x 5 x 5 = 625

The cafeteria has 2 choices of salads, 3 choices of entrees, and 2 choices of beverages. How many meal combinations are available and why?

• 7 because 2 + 3 + 2

• 12 because 2 x 3 x 2