Counting Principles and Combinatorics

Mr. Tarrou introduces the counting principle, permutations, and combinations, using a car building example to explain the counting principle. He then discusses lottery probability, highlighting the difference between permutations and combinations. The video concludes with formulas and examples to solidify understanding.

Which of the following subjects might introduce the concepts of Counting Principle, Permutations, and Combinations?

• Algebra 2

• Geometry

• Calculus

• Trigonometry

What is the total number of unique cars that can be built in the given car-building example?

• 25

• 20

• 15

• 30

In the car-building example, how many unique cars can be built with a manual transmission?

• 25

• 20

• 15

• 10

What is the fundamental counting principle used for?

• Determining the slope of a line

• Calculating the area of a circle

• Solving quadratic equations

• Finding the number of ways a sequence of events can occur

How many ways can six unique numbers be chosen from fifty-three in a lottery game?

• 53,000,000

• 1,000,000

• 22,957,480

• 16,529,385,600

In a lottery game, why are the odds of winning better than 1 out of 16.5 billion?

• Because there are fewer numbers to choose from

• Because the order of the numbers does not matter

• Because the lottery is rigged

• Because the numbers are replaced after each draw

What is the formula for calculating permutations?

• n! * r!

• n! / (n - r)! * r!

• n! / r!

• n! / (n - r)!

What is the formula for calculating combinations?

• n! * r!

• n! / (n - r)!

• n! / (n - r)! * r!

• n! / r!

When choosing three people from a group of twenty for a committee, which formula should be used?

• 20 nCr 3

• 20! / 3!

• 20! / (20 - 3)!

• 20 nPr 3

In a race with eighteen cars, how many ways can the first three cars cross the finish line?

• 18! / 3!

• 18 nCr 3

• 18 nPr 3

• 18! / (18 - 3)!