We distribute the 10 balls into 6 bins. If we randomly distribute the balls into the bins, what is the probability that all of the balls end up in the same bin? Is it just: (${10 \choose 1}*6)/ 6^{10}$
2026-03-26 14:28:06.1774535286
All balls fall into 1 bin
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The first ball can go in any of the bins ... but after that all other 9 need to go in the same bin, so the chances of that are $(\frac{1}{6})^9$
The fact that you have 10 balls does not multiply this by 10.