Final answer:
The number of ways Magnus can distribute 10 identical stickers among his 3 friends can be calculated using the stars and bars method, which results in 66 different ways using the combination formula C(12, 2).
Step-by-step explanation:
To find the number of ways that Magnus can give out 10 identical stickers to 3 of his friends, we can use the stars and bars method, which is a combinatorial technique used in determining the number of ways to distribute identical items among different containers. The problem can be visualized as having 10 identical stickers (stars) and 2 dividers (bars) to separate the stickers between the 3 friends. The arrangement of these stars and bars in a row represents a distribution of stickers to the friends.
To solve this problem, we look at the sequence consisting of the stickers and dividers. Since there are 10 stickers and 2 dividers, we have a total of 12 positions to fill. We need to select 2 positions out of these 12 to place the dividers, and this can be done in 12 choose 2 ways, which is calculated using the formula for combinations:
C(n, k) = n! / (k!(n - k)!) where n is the total number of items and k is the number of items to choose.
Thus, the number of ways Magnus can distribute the stickers is:
C(12, 2) = 12! / (2! * (12 - 2)!) = 66 ways.