You are making a recipe that consists of 5 different ingredients. In how many different orders can you add the ingredients to the bowl?
assuming you are using all the ingredients ...
5x4x3x2x1 = ....
or
5! =
To find the number of different orders in which you can add the 5 ingredients to the bowl, we need to calculate the number of permutations. A permutation is an arrangement of objects without repetition, where the order matters.
The formula to calculate the number of permutations is given by:
P(n, r) = n! / (n - r)!
Where:
- P(n, r) is the number of permutations of n objects taken r at a time.
- n! represents factorial n, which is the product of all positive integers up to n.
In your case, you have 5 different ingredients, and you want to find the number of different orders in which you can add them to the bowl. Therefore, n = 5 (the total number of objects) and r = 5 (the number of objects you are taking at a time).
P(5, 5) = 5! / (5 - 5)!
= 5! / 0!
Since 0! is equal to 1, we can simplify the equation to:
P(5, 5) = 5! / 1
= 5!
Calculating 5!:
5! = 5 x 4 x 3 x 2 x 1
= 120
Therefore, there are 120 different orders in which you can add the 5 ingredients to the bowl.