Question

Four acts are scheduled to perform in a variety show. How many different ways are there to schedule their appearances?

Answer 1

Hi! What have you tried so far?

Answer 2

(Also, welcome to OpenStudy!)

Answer 3

I tried to work it out

Answer 4

That's good. Do you have any ideas at all, or are you completely stuck?

Answer 5

(Being completely stuck is fine, by the way!) :)

Answer 6

completely stuck

Answer 7

Okay! Let's imagine that we're scheduling the acts, one slot at a time. We might start by deciding who's first, then after that we could decide who's second, then who's third, and then who's last.

Answer 8

How many options do we have, when deciding who's first?

Answer 9

four

Answer 10

Great!

Answer 11

Now imagine we've decided who's first.
How many options do we have left, when deciding who's second?

Answer 12

three

Answer 13

Well done :) So how about third and fourth?

Answer 14

? what do you mean

Answer 15

Well, if you imagine that we've chosen the first and second acts, how many options are left when deciding who's third?

Answer 16

two options

Answer 17

Great! And then how many options are left for the fourth act?

Answer 18

one

Answer 19

Well done! That means we had 4 options at the beginning, and then in each case we got 3 options, and then 2 options, and then 1 option. How do you think we might combine them to figure out our overall number of options?

Answer 20

(Clue: we don't want to add them up!)

Answer 21

4 x 3 x 2 x1

Answer 22

Excellent, well done!

Answer 23

so that is my answer? after I times

Answer 24

Yes, that's the answer!

Answer 25

ok thank you for your help

Answer 26

you're most welcome!