Question

How many different ways can a researcher select 5 rats from 20 rats and assign each to a different test?

Answer 1

`P_(20,5)=(20!)/((20-5)!)=(20!)/(15!)=1,860,480`

Explanation:

We are going to choose 5 rats from a population of 20 rats and each one will be in a different test. This means we care about the order of the pick, which makes this a permutation problem.

The general formula for a permutation is:

`P_(n,k)=(n!)/((n-k)!); n="population", k="picks"`

`P_(20,5)=(20!)/((20-5)!)=(20!)/(15!)`

And now let's evaluate it:

`(20xx19xx18xx17xx16xx15!)/(15!)=20xx19xx18xx17xx16=1,860,480`