A candy shop is unveiling a new line of candies made with real fruit juice. The candy will be available in 5 flavors. If they want to release one new flavor every week, in how many different orders can the flavors be released?
orders
The number of arrangements can be found using the formula for permutations:
n! / (n-r)!
where n is the total number of items and r is the number of items to be arranged.
In this case, there are 5 flavors and we want to release them one at a time. Therefore, n = 5 and r = 1.
Plugging the values into the formula, we get:
5! / (5-1)!
= 5! / 4!
= 5 x 4 x 3 x 2 x 1 / 4 x 3 x 2 x 1
= 5
Therefore, there are 5 different orders in which the flavors can be released.
wrong it is 120 becauseTo find out how many different orders are possible, use a factorial. A factorial is a whole number followed by an exclamation point. To evaluate a factorial, multiply all the whole numbers between 1 and the given number.
solve
The flavors can be released in 5! different orders.
5! = 5 × 4 × 3 × 2 × 1 = 120
The flavors can be released in 120 different orders.
You are correct. I apologize for my mistake. Thank you for providing the correct solution. The flavors can indeed be released in 5! = 120 different orders.
To calculate the number of different orders in which the flavors can be released, we need to use the concept of permutations. Since there are 5 flavors and they want to release them one at a time, we can calculate the number of permutations of 5 flavors taken all at a time.
The formula for calculating permutations is given by:
P(n, r) = n! / (n - r)!
Where:
n is the total number of items
r is the number of items taken at a time
! denotes factorial, which means multiplying all the whole numbers from 1 to the given number.
Using the formula, we can calculate the permutations of 5 flavors taken all at a time:
P(5, 5) = 5! / (5 - 5)!
= 5! / 0!
= 5! / 1
= 5 x 4 x 3 x 2 x 1 / 1
= 120
Therefore, there are 120 different orders in which the flavors can be released.