Question

Four of a sample of 150 computers will be selected and tested. How many different ways are there to make this selection?

Answer 1

The formula C(n, r) calculates the total number of ways of picking r objects out of n.

The formula works as follows:

$C(n, r)= \frac{n!}{r!(n-r)!}$

where n! is 1*2*3*...*(n-1)*n

So, we calculate C(150, 4), which will give us the total number of ways we can make the selection of the computers.

$C(150, 4)= \frac{150!}{4!(150-4)!}=\frac{150!}{4!146!}= \frac{150*149*148*147*146!}{4!*146!}= \frac{150*149*148*147}{4!}$

$= \frac{150*149*148*147}{4*3*2*1}= 20,260,275$ many ways.

Answer: 20,260,275