Question

Find the number of ways that Magnus can give out 12 identical stickers to 4 of his friends. (Not everyone has to get a sticker.)

Answer 1

[AI-generated answer — Bot GPT 3.5]

This problem can be solved using stars and bars method.

Let's represent the 12 stickers as stars: ************

Then, we can place 3 bars to separate the stickers into 4 groups for 4 friends to receive stickers.

For example, if we place the bars like this: |*|***|***|***|

It means that the first friend gets 1 sticker, the second friend gets 3 stickers, the third friend gets 3 stickers, and the fourth friend gets 5 stickers.

Therefore, the number of ways Magnus can give out 12 stickers to his 4 friends is:

12 + 4 - 1 choose 4 - 1 = 15 choose 3 = 455 ways.