There are 12 paintings in a show. How Many ways can the paintings take first second or third?
You have 12 paintings and you want to know how many ways you can place the paintings in 1st, 2nd and 3rd.
One way to think of this is to go "how many paintings can go in 1st place?" --> 12 paintings
Now that we have figured out 1st place, we can think of 2nd place. Remember that we already have 1 painting in 1st place and that same painting cannot be in 2nd place or 3rd place. So technically, we have 11 paintings that can be in 2nd place. Therefore when you think "how many paintings can go in 2nd place?" --> 11 paintings
Finally we need to think of how many paintings can be in 3rd place. Obviously we can't have a painting that is in 1st or 2nd place, right? So we have 10 paintings to choose from for our 3rd place. Therefore, "how many paintings can go in 3rd place?" --> 10 paintings
SO, the number of ways is equal to