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Mathematics

Set Theory

Fundamental Counting Principle

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If a password consists of 2 letters followed by 3 digits, how many unique passwords can be created? (Letters can repeat, digits can repeat)

You can create $26 \times 26 \times 10 \times 10 \times 10 = 676,000$ unique passwords.

You have 5 books to place on a shelf. How many different arrangements are possible?

There are $5! = 120$ different arrangements possible.

You have 3 different shirts and 4 different pairs of pants. How many unique outfits can you create?

You can create $3 \times 4 = 12$ unique outfits using the Fundamental Counting Principle.

A PIN number is composed of 1 letter (from A to Z) followed by 2 digits (from 0 to 9). How many unique PINs can be made?

There are $26 \times 10 \times 10 = 2,600$ unique PINs that can be made.

How many different ways can you arrange the letters in the word 'MATH'?

There are $4! = 4 \times 3 \times 2 \times 1 = 24$ different ways to arrange the letters.

A cafe offers 5 types of sandwiches and 3 types of drinks. How many different meal combinations can a customer order?

A customer can order $5 \times 3 = 15$ different meal combinations.

A chef has 4 different ingredients to choose from for an entrée and 2 different ingredients for a side. How many unique dish combinations can the chef create?

The chef can create $4 \times 2 = 8$ unique dish combinations.

You're rolling a six-sided die and flipping a coin. How many possible outcomes are there?

There are $6 \times 2 = 12$ possible outcomes.

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