There are 8 movies you would like to see currently showing in the theater. Due to time offerings, 2 of the movies must be seen first and second respectively.


A) In how many different ways can you want all the movies?

So, wouldn't that leave you with 6 items to arrange?

To solve this problem, we can use the concept of permutations. A permutation is an arrangement of objects in a specific order.

Since we have 8 movies to see, we need to choose 2 movies to be seen first and second. We can start by selecting 2 movies out of the 8 available options. This can be done using the formula for combinations, which is denoted as nCr, where n is the total number of objects and r is the number of objects to be selected. In this case, we need to find 2C2.

The formula for combinations is:

nCr = n! / (r!(n-r)!)

Applying this formula, we have:

2C2 = 2! / (2!(2-2)!)
= 2! / (2!0!)
= 2! / 2!
= 2

So, there are 2 ways to choose the 2 movies that must be seen first and second.

Once the first two movies are chosen, we have 6 remaining movies to be seen. The order in which we watch these 6 movies does not matter, as long as we have already seen the first two movies.

For the remaining 6 movies, we have 6! ways to arrange them. This can be calculated using the factorial formula:

6! = 6 x 5 x 4 x 3 x 2 x 1
= 720

So, there are 720 ways to arrange the remaining 6 movies.

Therefore, to find the total number of ways to watch all the movies, we multiply the number of ways to choose the first two movies (2) with the number of ways to arrange the remaining 6 movies (720):

Total number of ways = 2 x 720
= 1440

Therefore, there are 1440 different ways to watch all the movies.