A cooking recipe lists 6 ingredients which must be mixed in the correct order. Unfortunately the bottom of the page on which the correct order was given has been burnt off. Suppose that you make a guess at the correct order. What is the probabilty that you will be right?
Please help, I have no clue how to do this! Thanks!
Since the order matters, there are 6 different ingredients that could be used first.
Then there would be 5 remaining ingredients that could be used second.
Then there would be 4 remaining .... etc.
Number of ways = 6x5x4x3x2x1 = 720
(A string of consecutive multiplications such as 6x5x4x3x2x1 is called
6 factorial or 6!
Most calculators have a key called
n!
on mine, I press 6, then 2ndF n! )
To find the probability of guessing the correct order, we need to determine the total number of possible orders and the number of possible correct orders.
Let's assume that there are 6 distinct ingredients labeled A, B, C, D, E, and F. Since there are 6 ingredients, there are 6 choices for the first ingredient, 5 choices for the second ingredient, 4 choices for the third ingredient, and so on.
The total number of possible orders is given by the factorial of 6, denoted as 6!. It can be calculated as:
6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
Now, since we are guessing the correct order, there is only one correct order out of the total possible orders.
Therefore, the probability of guessing the correct order is:
P(correct order) = 1 / 720 ≈ 0.0014
So, the probability of guessing the correct order is approximately 0.0014, or 0.14%.
Note: This calculation assumes that each ingredient can only be used once in the recipe and that each ordering is equally likely.