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Find the number of ways that Magnus can give out $12$ identical stickers to $2$ of his friends, if every friend gets at least one sticker.

 May 26, 2024
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1. Give one sticker to each friend, leaving 10 stickers to distribute.

 

2. Imagine the remaining 10 stickers as stars and 1 separator bar.

 

3. You have a total of 10 stars and 1 bar to divide the stickers.

 

4. Use the formula "n + k - 1 choose k - 1" where n is the number of stars and k is the number of bars.

 

5. Plug in n = 10 and k = 2 into the formula.

 

6. The number of ways to distribute the stickers among friends is 11.

 

Therefore, Magnus can give out the 12 identical stickers to his 2 friends in 11 different ways, ensuring each friend receives at least one sticker.

 May 26, 2024

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