#1: Bill is renting DVDs from the video store. He must choose 3 DVDs from a list of 8 new releases and then decide in what order to watch them. how many different schedules of videos can he create, if he cannot watch the same movie more than once?

a) 24
b) 56
c) 72
d) 336
e) 512

I don't get why the answer is 336. I understand that there are 8 dvds to choose from for the first of three dvd then 7 dvds to choose from then 6 dvds to choose from resulting in 8*7*6. What confused me is "and then decide in what order to watch them." part.

The 3 dvds can be ordered in 3*2*1 = 6

So shouldn't the overall possibilities be 336 * 6?

By following the method "8 choices for the first", "7 choices for the second", "6 choices for the third" we are accounting for the order in which the DVD's will be watched.

-- Veritas Help

If we were simply choosing 3 dvds from 8 and the order did not matter we would use the combinations formula.

8!/(3!(8-3)!)

= 8*7*6/(3*2*1) = 56 ways to choose 3 from 8


Once we have our 3 selected, we have 3*2*1 = 6 ways to sequence how we watch them.

- Veritas Help