Understanding Combination Locks and Permutations

The video tutorial explains how a combination lock works and why it should be called a permutation lock since the order of numbers matters. It demonstrates how to calculate the number of possible lock permutations using the formula for permutations, 30 permute 3, which equals 24,360. The tutorial also verifies this calculation using the multiplicative principle and a calculator, emphasizing the importance of distinct numbers in the process.

What is the first step in opening a combination lock?

• Turn the dial to the left to the second number

• Turn the dial to the right to the first number

• Turn the dial to the right to the third number

• Turn the dial to the left to the first number

What is the significance of the numbers being distinct in a combination lock?

• It allows for repeated numbers

• It increases the number of possible combinations

• It ensures each number is used only once

• It makes the lock easier to open

Why is the term 'combination lock' considered misleading?

• Because the numbers do not need to be distinct

• Because it uses letters instead of numbers

• Because the order of numbers does not matter

• Because the order of numbers does matter

What is the formula for calculating permutations?

• n factorial divided by k factorial

• n factorial divided by (n minus k) factorial

• k factorial divided by n factorial

• n plus k factorial

How many different lock permutations are possible with 30 numbers?

• 24,360

• 29,400

• 28,560

• 30,000

What does simplifying 27 factorial divided by itself result in?

• 1

• 0

• 27

• 30

What is the first event in the multiplicative principle approach?

• Selecting the third number

• Selecting the second number

• Selecting the first number

• Calculating the factorial

How many choices are there for the second number in the multiplicative principle?

• 27

• 29

• 28

• 30

What is the result of 30 times 29 times 28?

• 25,000

• 24,360

• 23,940

• 26,280

Which principle is used as an alternative method to calculate permutations?

• Divisive principle

• Multiplicative principle

• Additive principle

• Subtractive principle