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 .

Step-by-step 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 :

⇒ $nP_r= \frac{n!}{(n-r)!}$

According to question , we have

⇒ $15P_4= \frac{15!}{(15-4)!}$

⇒ $15P_4= \frac{15!}{(11)!}$

⇒ $15P_4= \frac{15(14)(13)(12)11!}{(11)!}$

⇒ $15P_4= 15(14)(13)(12)$

⇒ $15P_4= 32,760$

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