Question

Tanisha is picking out some movies to rent, and she is primarily interested in mysteries and foreign films. She has narrowed down her selections to 17 mysteries and 8 foreign films. Step 1 of 2: How many different combinations of 4 movies can she rent?

Answer 1

Tanisha can create 34,650 different combinations of 4 movies from her selection of 17 mysteries and 8 foreign films, calculated using the combination formula.

Step-by-step explanation:

Calculating Movie Rental Combinations

Tanisha is interested in picking out a combination of 4 movies to rent out of a total selection consisting of 17 mysteries and 8 foreign films. To calculate the number of different combinations of 4 movies she can rent, we will use the combination formula which is defined as C(n, r) = n! / [r!(n - r)!], where 'n' represents the total number of items to choose from, 'r' is the number of items to choose, and '!' denotes factorial.

First, we calculate the total number of films by adding the mysteries and foreign films: 17 mysteries + 8 foreign films = 25 films. She is choosing 4 out of these, so n=25 and r=4. The factorial of a number is the product of all positive integers less than or equal to that number (e.g., 5! = 5 x 4 x 3 x 2 x 1 = 120).

To find the combinations of 4 films out of 25, we use the combination formula:

C(25, 4) = 25! / [4!(25 - 4)!] = 25! / [4! x 21!]

Now we can simplify the factorials by canceling out the common terms in the numerator and the denominator:

C(25, 4) = (25 x 24 x 23 x 22) / (4 x 3 x 2 x 1)

= (25 x 6 x 23 x 11) / (2 x 1)

= 25 x 6 x 23 x 11

= 34,650

Tanisha has 34,650 different combinations of 4 movies from her selection of mysteries and foreign films.