Raj is to select six chocolates from a tray containing the chocolates of type (i) fruit & nut, (ii) roasted almond, (iii) milky-bar, (iv) blueberry. All chocolates of each type are identical. There are at least six chocolates of each of these four types in the tray. How many different assortments of six chocolates can be selected?

An assortment is fixed by how many chocolates of each type are chosen, that is, by non-negative integers $$x_1 + x_2 + x_3 + x_4 = 6$$, and the supply of at least 6 per type puts no extra limit. By the stars and bars method the number of solutions is $$\binom{6 + 4 - 1}{4 - 1} = \binom{9}{3}$$. Since $$\binom{9}{3} = \frac{9 \times 8 \times 7}{3 \times 2 \times 1} = 84$$, Raj can select 84 different assortments.