Fundamental Counting Principle and Sample Space

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 license plate numbers consisting of three letters followed by three numbers are possible when repetition is allowed?

• 26 x 26 x 26 x 10 x 10 x 10 = 17576000

• 26 x 25 x 24 x 10 x 9 x 8 = 11232000

• 26 x 26 x 26 x 9 x 9 x 9 = 12812904

• 26 x 25 x 24 x 9 x 8 x 7 = 7862400

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

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

A seven-question quiz has 4 true/false questions followed by 3 multiple choice questions. For each multiple choice question there are four possible answers. In how many different ways is it possible to answer the seven questions?

• 12

• 80

• 28

• 1024

Harpo, Groucho, Chico, Zeppo, Gummo and Karl are running in a race. How many different orders of finish are possible?

• 36

• 64

• 720

• 46656

If you draw a random card from a standard deck of cards, how many possible outcomes?

• 13

• 26

• 52

• 54

The cafeteria is serving three kinds of sandwiches:  tuna (T), chicken, (C), and peanut butter (P).  They are also serving a choice of two drinks:  milk (M) or water (W).  Which shows the complete set of possible combinations?

• TW, CW, PW

• TW, TM, TC, CW, PW

• TW, TM, CW, CM, PW, PM

• TCP, MW