Combinations and Permutations Concepts

The video tutorial explains how to calculate the number of different choices a player has in a lottery game where they pick five numbers from zero to nine without repetition. It covers both scenarios where order matters (permutations) and where order does not matter (combinations). The tutorial provides step-by-step calculations for both permutations and combinations, using factorials, and verifies the results using a calculator.

In a lottery game, how many numbers does a player pick from?

• Six

• Five

• Ten

• Nine

What is the key difference between permutations and combinations?

• Combinations allow repetition, permutations do not.

• Permutations consider order, combinations do not.

• Combinations consider order, permutations do not.

• Permutations allow repetition, combinations do not.

How do you calculate 10 permute 5?

• 5 factorial divided by (10-5) factorial

• 5 factorial divided by 10 factorial

• 10 factorial divided by (10-5) factorial

• 10 factorial divided by 5 factorial

What is the result of 10 permute 5?

• 5040

• 120

• 252

• 30240

How is 10 choose 5 calculated?

• 10 factorial divided by (10-5) factorial

• 5 factorial divided by 10 factorial

• 10 factorial divided by 5 factorial

• 10 factorial divided by (5 factorial times 5 factorial)

What is the result of 10 choose 5?

• 30240

• 5040

• 252

• 120

Which mathematical operation is used to simplify 10 and 5 in the combination calculation?

• Addition

• Division

• Subtraction

• Multiplication

What common factor is shared between 10 and 5 in the combination calculation?

• 7

• 2

• 3

• 5

In the combination calculation, which numbers are simplified out in the denominator?

• 5 and 10

• 3 and 9

• 4 and 2

• 7 and 6

What is the final product of the simplified combination calculation?

• 252

• 5040

• 120

• 30240