Algebra 2: Final Exam Review

What is the value of 3!?

What is the value of 4!/2!?

What is the value of 7C2?

What is the value of 4C3 + 6C5?

What is the value of 6P2?

Are the two events of randomly selecting a student and then another student from the same class independent or dependent?

Are the two events of tossing a number cube to select a number, and then tossing it again to select another number independent or dependent?

How many ways can you choose 3 food items for the first dinner if you bring 12 food items?

How many different combinations of food can you make if the cafeteria offers 4 sandwiches, 3 sides, 2 desserts, and 5 drinks?

How many ways can you arrange 8 file folders?

Factorial and Combinations

3! (factorial) equals 6, calculated as 3 × 2 × 1.
4!/2! equals 12, derived from the formula for combinations where 4! represents total arrangements divided by 2! for the arrangement of 2 items.
7C2 (combinations) gives 21; it counts the ways to choose 2 out of 7 without regard for order.

Additional Combinations

4C3 + 6C5 equals 10; combines two different combinations from distinct groups.
6P2 (permutations) equals 30, indicating the number of ways to arrange 2 items from 6 distinct options.

Probability: Independent vs. Dependent Events

Randomly selecting a student and then another from the same group is a dependent event, as the first selection affects the second's options.
Selecting a number by rolling a die twice constitutes independent events because the outcome of the first roll does not influence the result of the second.

Combinatorial Choices

Choosing 3 items from 12 for the first dinner can be done in 220 ways, illustrating the concept of combinations in selecting a subset.
A cafeteria menu with 4 sandwiches, 3 sides, 2 desserts, and 5 drinks results in a total of 120 unique meal combinations available for selection.

Arranging Items

Arranging 8 file folders in a drawer results in 40,320 different configurations, emphasizing the importance of factorial calculations in permutations.

This quiz reviews key concepts in Algebra 2, focusing on permutations, combinations, and independence of events. Each flashcard presents a problem or concept that is essential for mastering the material covered in the final exam. Test your knowledge and preparation for Algebra 2!