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José is on a gameshow that involves a taste test. He gets to see a list of 15 different secret ingredients before
tasting 3 dishes one after the other. The 3 dishes are all identical to each other except that each dish contains 1
of the 15 secret ingredients. He gets 60 seconds to identify what secret ingredient was in each dish.

The permutation formula nPr can be used to find the number of unique ways to arrange the ingredients in the
dishes.

What are the appropriate values of n and r?

Answer :

Using the permutation formula, it is found that:

  • The appropriate value of r is 3.
  • The appropriate value of n is 15.
  • There are 2730 ways to arrange the dishes.

Permutation formula:

The number of possible arrangements of r elements from a set of n elements is given by:

[tex]nPr = P_{(n,r)} = \frac{n!}{(n-r)!}[/tex]

In this problem:

  • 3 elements from a set of 15, thus the appropriate values are [tex]n = 15, r = 3[/tex].

The number of ways is:

[tex]P_{15,3} = \frac{15!}{12!} = 2730[/tex]

A similar problem is given at https://brainly.com/question/24245547

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