Fundamental Counting Principle

Find the number of possible outcomes.

When the spacebar is pressed, a computer program outputs a random even number greater than 2 and less than 12. You press the button once.

• 10

• 11

• 5

• 4

How many five-digit numbers can be formed if the leading digit and the last digit cannot be a zero?

• 8,100

• 59,049

• 81,000

• 100,000

DNA molecules include the base units adenine, thymine, cytosine, and guanine (A, T, C, and G). The sequence of base units along a strand of DNA encodes genetic information. In how many different sequences can A, T, C, and G be arranged along a short strand of DNA that has only 6 base units?

• 48

• 572

• 4,096

• 65,536

From a standard deck of cards, how many ways can you pick an ace, a heart, and then a spade?

Provided you put the cards back into the deck.

• 52

• 208

• 169

• 676

How many positive even integers less than 100,000 can be written using the digits 3, 6, 7, and 0?

• 126

• 512

• 100,000

• 1,000

In how many different ways can a 8-question true-false test be answered if every question must be answered?

• 512

• 256

• 1,024

• 16

How many odd 2-digit positive integers greater than 30 are there?

• 45

• 50

• 35

• 70

You are taking a survey on your experience at McDonald's. For the first four questions you can answer Below Average, Average, or Above Average for each question. The last four questions you can respond with either Agree or Disagree. How many total outcomes are there for this survey?

• 96

• 1,024

• 1,296

• 4,000

A single die is rolled. How many ways can you roll a number less than 4, then an even, and then an odd?

• 4

• 18

• 27

• 36

A baseball manager is determining the batting order for the team. The team has 9 players, but the manager definitely wants the pitcher to bat last. How many batting orders are possible?

• 387,420,489

• 36,000

• 362,880

• 40,320