How to count
(a) Find the number of ways that Magnus can give out 20 identical stickers to 5 of his friends. (Not everyone has to get a sticker.)
(b) Find the number of ways that Magnus can give out 20 identical stickers to 5 of his friends, if every friend gets at least one sticker.
+2668 a) There are 20 stars and 4 bars, so there are \({20 + 4 \choose 4} = \color{brown}\boxed{10,626}\) ways to give out the stickers
+2668 b) Start by giving each kid a sticker. Now, there are 15 stars and 4 bars for \({15 + 4 \choose 4} = \color{brown}\boxed{3,876}\) cases
