Hello, qazxsw11111!

A box contains 5 white balls, 3 red balls and 2 green balls.

Three balls are taken from box with replacement.

My work:

My explanation is that a white, red or green ball must be taken

and there are 3! ways of arranging the 3 scenarios.

Correct!

Five balls are taken without replacement.

My wrong method:

This probability cannot be correct since it is above 1.

What is the loophole that I did not see?

We want 2 Whites and 3 Others.

There are: . scenarios ... not 120.