Out of 13 objects, 4 are indistinguishable and rest are distinct. The number of ways we can choose 4 objects out of 13 objects is _____________.

As there are total 13 toys and 4 indistinguishable , hence 13-4 = 9 distinct toys are present.

Since the toys are indistinguishable , we can pick 5 combinations of (indistinguishable, distinct) : (0,4)/(1,3)/(2,2)/(3,1),/(4,0)

Hence, the question can be solved by focusing on no of ways to pick 'n' distinct balls out of 9 balls for n = {4,3,2,1,0}

Total possibilities = $$9C_4+9C_3+9C_2+9C_1+9C_0$$

                          =  126 + 84 + 36 + 9 + 1 = 256

Therefore, the answer is 256.