Final answer:
Tanisha can rent movies in three scenarios, each requiring a different combination calculation: 2 mysteries with 2 foreign films, 3 mysteries with 1 foreign film, or 4 mysteries. The total number of combinations is the sum of the combinations calculated for each scenario.
Step-by-step explanation:
Tanisha is interested in renting movies and has a choice of 17 mysteries and 8 foreign films. We want to find the number of different combinations of 4 movies she can rent, given that she wants at least two mysteries. This question can be solved using the concepts of combinations in mathematics.
Here are the possible scenarios for Tanisha's rental choices:
- She rents 2 mysteries and 2 foreign films.
- She rents 3 mysteries and 1 foreign film.
- She rents 4 mysteries.
To calculate the total number of combinations, we will use the combination formula C(n, k) = n! / (k! * (n-k)!), where 'n' is the total number of items to choose from, 'k' is the number of items to choose, and '!' denotes factorial.
The number of combinations for each scenario is:
- C(17, 2) * C(8, 2) for 2 mysteries and 2 foreign films (Scenario 1)
- C(17, 3) * C(8, 1) for 3 mysteries and 1 foreign film (Scenario 2)
- C(17, 4) for 4 mysteries (Scenario 3)
To find the total number of combinations, we add the number of combinations for each scenario together. Therefore, Tanisha's total number of possible combinations is the sum of the number of combinations for each scenario.