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)= (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)= (150!)/(4!(150-4)!)=(150!)/(4!146!)= (150*149*148*147*146!)/(4!*146!)= (150*149*148*147)/(4!)`


`= (150*149*148*147)/(4*3*2*1)= 20,260,275` many ways.

Answer: 20,260,275