Question

A couple has 10 movies in their Netflix queue. They decide to randomly choose 2 movies from the queue. How many possible 2-movie selections are there?

Answer 1

There are 45 possible 2-movie selections from 10 movies in the couple's Netflix queue, calculated using the combination formula for a combination of 10 taken 2 at a time.

Step-by-step explanation:

The student is asking about the number of ways to select 2 movies from a queue of 10 movies. This is a problem of combinations where order does not matter and can be solved using the combination formula C(n, k) = n! / (k!(n-k)!), where n is the total number of movies, and k is the number of movies to select.

To calculate the number of possible 2-movie selections, we use the formula with n=10 and k=2:

C(10, 2) = 10! / (2!(10-2)!) = 10! / (2!8!)

This simplifies to:

10 × 9 / (2 × 1) = 45

Therefore, there are 45 possible 2-movie selections that the couple can choose from.

Answer 2

Given:

A couple has 10 movies in their Netflix queue. They decide to randomly choose 2 movies from the queue.

So, the order is not important for the given situation

So, we will use the combinations

So, the number of possible 2-movie selections will be as follows:

`^(10)C_2=(10!)/((10-2)!\cdot2!)=(10\cdot9\cdot8!)/(8!\cdot2!)=(90)/(2)=45`

So, the answer will be there are 45 possible ways