Miyu is giving out 9 identical chocolates to her 7 friends, including Dhruv. All possible distributions are equally likely. What is the probability that Dhruv gets exactly 2 chocolates?
+2666 9 chocolates, 7 friends = 9 stars, 6 bars. So, there are \({15 \choose 6} = 5005 \) combinations.
If Dhruv gets 2, there are 5 chocolates for 6 people, which means there are 7 stars and 5 bars, making for \({12 \choose 5} = 792\) cases
So, the probabilty is \({792 \over 5005} = \color{brown}\boxed{72 \over 455}\)
