Statement-1: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is 9C3.
Statement-2: The number of ways of choosing any 3 places from 9 different places is 9C3.
Solutions · 1
Official solution
By the stars-and-bars method, distributing 10 identical balls into 4 distinct non-empty boxes gives (4−110−1)=(39) --- so Statement 1 is true.
Statement 2 is also true as a standalone combinatorial fact, but it does not directly explain the balls-in-boxes result (the connection requires the stars-and-bars bijection, not simply "choosing 3 places from 9").