Question

How many different ways can a researcher select 4 rats from 15 rats and assign each to a different test?

Answer 1

By 32,760 different ways can a researcher select 4 rats from 15 rats and assign each to a different test .

Explanation:

We need to find How many different ways can a researcher select 4 rats from 15 rats and assign each to a different test.Let's find out:

We will use Permutation here : As we will chose 4 rats out of 15 rats , order will be considered which will make this as a permutation problem . Formula for permutation is given by :

⇒
`nP_r= (n!)/((n-r)!)`

According to question , we have

⇒
`15P_4= (15!)/((15-4)!)`

⇒
`15P_4= (15!)/((11)!)`

⇒
`15P_4= (15(14)(13)(12)11!)/((11)!)`

⇒
`15P_4= 15(14)(13)(12)`

⇒
`15P_4= 32,760`

Therefore , By 32,760 different ways can a researcher select 4 rats from 15 rats and assign each to a different test .