The video tutorial explains how to calculate the probability of winning a lottery game where a player selects 4 numbers from 1 to 60. It covers the concept of combinations, using a formula involving factorials to determine the number of possible outcomes. The tutorial then calculates the probability of a specific set of numbers winning by dividing one successful outcome by the total number of combinations.

In the lottery game described, how many numbers does a player choose from?

• 60

• 30

• 40

• 50

What is the main difference between combinations and permutations?

• Neither consider order.

• Both consider order.

• Permutations consider order, combinations do not.

• Combinations consider order, permutations do not.

What is the formula used to calculate combinations?

• n factorial divided by (n-r) factorial

• n factorial divided by r factorial

• n factorial divided by (n-r) factorial times r factorial

• n factorial times r factorial

Why do we divide by 4 factorial in the combination formula?

• To account for the number of ways to arrange four numbers.

• To increase the number of combinations.

• To account for the number of ways to arrange three numbers.

• To simplify the calculation.

What is the simplified expression for 60 factorial divided by 56 factorial?

• 60 times 59 times 58

• 60 times 59

• 60

• 60 times 59 times 58 times 57

What is the total number of combinations possible when choosing 4 numbers from 60?

• 600,000

• 450,000

• 500,000

• 487,635

Tags

CCSS.HSS.CP.B.9

What is the probability of winning with the numbers 3, 15, 46, and 49?

• 1 in 487,635

• 1 in 500,000

• 1 in 600,000

• 1 in 450,000

How many possible outcomes are there in the lottery game?

• 50,000

• 100,000

• 1,000,000

• 487,635

What does the number 487,635 represent in the context of the lottery game?

• The total number of players.

• The total number of possible combinations.

• The total number of possible permutations.

• The total number of winning numbers.

Why is the probability of winning with a specific set of numbers so low?

• Because the numbers are not replaced.

• Because the game is rigged.

• Because the numbers are chosen randomly.

• Because there are many possible combinations.