How many ways can a person select 3 movies to rent from the top ten rentals? Arrange them into a triple feature?
Number of ways to select them = C(10,3) = 120
Number of ways to arrange them = 10x9x8 = 720
To determine the number of ways a person can select 3 movies from a total of 10 movies, we can use the concept of combinations. The number of combinations of 10 movies taken 3 at a time can be calculated using the formula:
nCr = n! / ((n-r)! * r!)
Where "n" is the total number of movies (10) and "r" is the number of movies selected (3). The exclamation mark (!) denotes the factorial of a number.
Using this formula, we can calculate the number of combinations as follows:
10C3 = 10! / ((10-3)! * 3!)
= 10! / (7! * 3!)
= (10 * 9 * 8) / (3 * 2 * 1)
= 120
Therefore, there are 120 different ways to select 3 movies from the top ten rentals.
To arrange them into a triple feature, we can find the number of permutations of those 3 movies. The number of permutations of a set of 3 movies is given by:
nPr = n! / (n-r)!
Using this formula:
3P3 = 3! / (3-3)!
= 3! / 0!
= 3! / 1
= 3
Therefore, there are 3 ways to arrange the selected 3 movies into a triple feature.
To determine the number of ways to select 3 movies to rent from the top ten rentals and arrange them into a triple feature, we can use the concept of combinations and permutations.
First, let's find the number of ways to select 3 movies from the top ten rentals, ignoring the order in which they will be watched. This is a combination problem.
To calculate the number of combinations, we use the formula:
C(n, r) = n! / (r! * (n-r)!)
Where n is the total number of items (in this case, 10 movies), and r is the number of items to be selected (in this case, 3 movies).
So, the number of ways to select 3 movies from the top ten rentals is:
C(10, 3) = 10! / (3! * (10-3)!) = 10! / (3! * 7!) = (10 * 9 * 8) / (3 * 2 * 1) = 120
There are 120 ways to select 3 movies from the top ten rentals, disregarding the order.
Now, let's consider the order in which the movies will be watched, creating a triple feature. This is a permutation problem.
To calculate the number of permutations, we use the formula:
P(r) = r!
Where r is the number of items to be arranged (in this case, 3 movies).
So, the number of ways to arrange the 3 selected movies into a triple feature is:
P(3) = 3! = 3 * 2 * 1 = 6
There are 6 ways to arrange the 3 selected movies into a triple feature, considering the order.
Therefore, the number of ways to select 3 movies to rent from the top ten rentals and arrange them into a triple feature is the product of the combinations and permutations:
120 * 6 = 720
There are 720 ways to select 3 movies from the top ten rentals and arrange them into a triple feature.