Fundamental Counting Principal #2

What is the Fundamental Counting Principle?

• The Fundamental Counting Principle is a rule in geometry that calculates the area of shapes.

• The Fundamental Counting Principle is a rule in statistics that analyzes data trends.

• The Fundamental Counting Principle is a rule in algebra that simplifies complex equations.

• The Fundamental Counting Principle is a rule in combinatorics that allows you to determine the total number of outcomes for a sequence of events.

Explain how permutations of a set differ from combinations.

• In permutations, the order matters, while in combinations, it does not.

• Permutations always involve all elements of the set, while combinations can involve a subset.

• In permutations, the order does not matter, while in combinations, it does.

• Permutations involve repetition of elements, while combinations do not.

Calculate the number of ways to arrange the letters in the word 'MATH'.

• 24

• 12

• 16

• 20

In how many ways can the letters in the word 'MISSISSIPPI' be arranged?

• 28900

• 34650

• 24560

• 40230

What is the factorial notation for 5?

• 24

• 50

• 120

• 150

A committee of 4 people is to be formed from a group of 10. How many different committees can be formed?

• 210

• 120

• 45

• 15

How many ways can the letters in the word 'COMPUTER' be arranged if the vowels must always be together?

• 360

• 504

• 620

• 720

Explain the concept of permutations with repetition using an example.

• Permutations with repetition only allow for unique elements to be used in the arrangement

• Permutations with repetition allow for the same element to be used multiple times in the arrangement.

• Permutations with repetition do not involve the concept of order

• Permutations with repetition result in a fixed number of arrangements

In how many ways can the letters in the word 'ALGORITHM' be arranged if the vowels must occupy the odd positions?

• 5040

• 2160

• 4320

• 3600

A password consists of 4 digits, where each digit can be 0-9. How many different passwords are possible?

• 9999

• 1234

• 0000

• 10000