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- 1. Multiple Choice
The fundamental counting principle
Tells you the probability of an event.
Tells you how many different possible outcomes there are.
Helps you convert a fraction into a percent.
Shows you the outcomes that don't appear in a tree diagram.
- 2. Multiple Choice
If I use the fundamental counting principle, how many different outcomes are there if I flip 4 different 2-sided coins?
8, because 4 x 2 = 8
6, because 4 + 2 = 6
16, because 2 x 2 x 2 x 2 = 16
256, because 4 x 4 x 4 x 4 = 256
- 3. Multiple Choice
Using the fundamental counting principle, how many different outcomes could you have if you rolled 4 different six-sided dice?
1,296, because 6 x 6 x 6 x 6 = 1,296
24, because 6 x 4 = 24
36, because it 6 x 6 = 36
360, because 6 x 5 x 4 x 3 = 360
- 4. Multiple Choice
Use the fundamental counting principle to find the total number of outcomes (or outfits) if you have a suitcase with 5 different shirts, 3 types of jackets, 2 different pants, and 3 types of shoes.
13, because 5 + 3 + 2 + 3 = 13
120, because 5 x 4 x 3 x 2 =120
90, because 5 x 3 x 2 x 3 = 90
52, because (5 + 3 + 2 + 3) x 4 = 52
- 5. Multiple Choice
Use the fundamental counting principle to find the total number of possible outcomes for my smartphone lock screen if I have to use 4 different numbers from 0-9, and I can reuse numbers. (For instance, I could use "1111")
6,561, because 9 x 9 x 9 x 9 = 6,561
5,040, because 10 x 9 x 8 x 7 = 5,040
10,000, because 10 x 10 x 10 x 10 = 10,000
1111, because that's the number in the problem.
- 6. Multiple Choice
Using the fundamental counting principle, how many different possible codes are there to lock my iPhone if I use 4 digits, each digit has to be a number from 0-9, and I cannot use the same number twice? (For instance, I could use codes like 1234)
5,040, because 10 x 9 x 8 x 7 = 5,040
1234, because that's the number in the problem
10,000 because 10 x 10 x 10 x 10 = 10,000
40, because 10 + 10 + 10 + 10 = 40
- 7. Multiple Choice
Use the fundamental counting principle to find all the different types of 1-topping pizzas are possible if you could choose from 4 types of crusts, 5 types of cheese, 2 sauces, and 10 types of toppings.
21, because 4 + 5 + 2 + 10 = 21
84, because (4 + 5 + 2 + 10) x 4 = 84
1, because it's a 1-topping pizza
400, because 4 x 5 x 2 x 10 = 400
- 8. Multiple Choice
Use the fundamental counting principle to find the total number of possible outcomes for lunch if you can choose from 4 types of sides, 6 types of main entree, and 12 types of drinks.
3, because you are choosing 1 side, 1 entree, and 1 drink.
22, because 4 + 6 + 12 = 22
66, because (4 + 6 + 12) x 3 = 66
288, because 4 x 6 x 12 = 288
- 9. Multiple Choice
Use the fundamental counting principle to find the total number of outcomes for an election if there are 3 different positions and there are 8 people running for the positions. Remember, one position can only be held by one person.
24, because 3 x 8 = 24
81, because 3 x 3 x 3 x 3 = 81
4,096, because 8 x 8 x 8 x 8 = 4,096
1,680, because 8 x 7 x 6 x 5
- 10. Multiple Choice
Use the fundamental counting principle to find the total number of different outcomes for a car license plate if you need 3 different letters and 3 different 1-digit numbers. You can reuse numbers and letters (for instance, AAA-111 is possible). There are 26 letters in the alphabet, 1-digit numbers are 0-9.
6, because there are six different spaces in the license plate.
17,576,000, because 26 x 26 x 26 x 10 x 10 x 10
12,812,904, because 26 x 26 x 26 x 9 x 9 x 9
9, because 3 x 3
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