Question

8. Describe a situation that could be modeled by using 5P2.

Answer 1

See explanation and example below.

Explanation:

By definition permutation is the "act of arranging the members of a set into a sequence or order, or, if the set is already ordered, reordering its elements"

And we use it when we want to find how many ways we can select combinations from n elements with and order between the elements.

The permutation formulas is given by:

`nPx = (n!)/((n-x)!)`

Example 1 : Let's suppose that a license plate begins with two letters. If the possible letters are X, Y, Z, W and A, how many different permutations of these letters can be made if no letter is used more than one time?

For this case we can apply permutations since we want a letter no more than one time, so we can find the number of ways like this:

`5P2 = (5!)/((5-2)!)= (5!)/(3!)=(5*4*3!)/(3!)= 20`

Example 2: In how many ways can a governor, a secretary and a arquitect be chosen from among 5 candidates?

The problem involves 5 candidates taken 2 at a time so then we can apply permutations for this case

`5P2 = (5!)/((5-2)!)= (5!)/(3!)=(5*4*3!)/(3!)= 20`