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Fundamental Counting Principle Challenge

Quiz

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Engaging FCP quiz game

Created by

Philippines

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Fundamental Counting Principle Challenge
 

Fundamental Counting Principle ChallengeOnline version

Engaging FCP quiz game

by JAN NATHANIEL CARAAN
1

If a vending machine offers 3 drinks and 4 snacks, how many distinct combos exist (one drink and one snack)?

2

You have 5 shirts and 3 pairs of pants. How many outfits can you create (one shirt and one pants)?

3

A password uses 2 letters followed by 3 digits. How many possible passwords exist?

4

A menu has 2 soups, 3 sandwiches, and 2 drinks. How many single-item combos?

5

A quiz has 4 questions, each with 5 options. How many ways to answer all questions?

6

A playlist has 3 genres, 4 artists, and 2 moods. How many unique playlists (one from each)?

7

A lock has 6 possible first digits and 5 possible second digits. How many two-digit codes are possible?

8

A badge design can be chosen in 4 colors, 3 shapes, and 2 sizes. How many distinct designs?

9

If a student selects one topic from 3 math topics and one from 4 science topics, how many study plans exist?

10

A T-shirt comes in 3 colors and 3 sizes. How many color-size combos exist?

Feedback

Using FCP: 3 options for drink × 4 for snack = 12 total outcomes.

Total outfits = 5 × 3 = 15.

26^2 × 10^3 = 676 × 1000 = 676000.

Total items = 2 × 3 × 2 = 12.

4 categories? No—each of 4 questions has 5 choices: 5^4 = 625.

3 × 4 × 2 = 24.

6 × 5 = 30.

4 × 3 × 2 = 24.

3 × 4 = 12.

3 × 3 = 9.

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