Arrangements and Combinations in Mathematics

The video tutorial covers the concept of simple arrangements, using a student council example to explain how different groupings can be formed. It defines simple arrangements, introduces the formula, and provides examples to illustrate the concept. The tutorial also discusses complex arrangements and calculations, and concludes with solving equations involving arrangements.

In the example of the student council election, how many different groups can be formed with 4 students for 2 positions?

• 12

• 10

• 8

• 6

What is the principle used to calculate the number of arrangements?

• Addition Principle

• Subtraction Principle

• Division Principle

• Multiplication Principle

Which of the following is true for simple arrangements?

• Elements are not distinct

• Order matters

• Elements are repeated

• Order does not matter

How many possibilities are there if you need to choose 3 students out of 5 for different positions?

• 90

• 60

• 30

• 120

What differentiates an arrangement from a combination?

• The number of elements

• The order of elements

• The type of elements

• The total number of elements

If a school has 18 teachers and needs to select a director, a vice-director, and a coordinator, how many different ways can this be done?

• 3,456

• 4,896

• 5,760

• 6,720

How many different ways can the word 'LIVRO' be painted using 8 different colors, one for each letter?

• 4,320

• 3,600

• 5,040

• 6,720

If two people enter a van with 7 available seats, how many different ways can they sit?

• 42

• 35

• 28

• 21

What is the value of X if the arrangement formula gives X(X-1) = 30?

• 6

• 4

• 5

• 7

In the context of arrangements, what does the term 'hierarchy' refer to?

• The importance of order

• The total number of groups

• The distinct nature of elements

• The number of elements