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Find the number of ways that Magnus can give out $12$ identical stickers to $2$ of his friends. (Not everyone has to get a sticker.)

 May 26, 2024
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To find the number of ways Magnus can give out 12 identical stickers to 2 of his friends, we can use a concept from combinatorics called "stars and bars." We represent the 12 stickers as 12 stars (*...), and we need to divide them among 2 friends by placing 1 divider between the stars for the first friend to receive the stickers and 1 divider between the stars for the second friend to receive the stickers.
 

For example, if Magnus gives all 12 stickers to the first friend, it would look like this: || (where * represents a sticker and | represents a divider). The number of ways to distribute the stickers can be calculated using the formula: n + k choose k, where n is the number of stars (stickers) and k is the number of dividers (friends). In this case, n = 12 stickers and k = 2 friends. Plugging these values into the formula: 14 choose 2 = 14! / (2! 12!) = 14 13 / (2 * 1) = 91

 

Therefore, Magnus can give out the 12 identical stickers to his 2 friends in 91 different ways.

 May 26, 2024

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