Statement - 1 : The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is $$^9{C_3}.$$
Statement - 2 : The number of ways of choosing any 3 places from 9 different places is $$^9{C_3}.$$

Solution :
The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box empty is same as the number of ways of selecting $$(r - 1)$$  places out of $$(n - 1)$$  different places, that is $$^{n - 1}{C_{r - 1}}.$$
Hence required number of ways $$^{10 - 1}{C_{4 - 1}} = {\,^9}{C_3}$$
∴ Both statements are correct and second statement is a correct explanation of statement - 1.