If we want to pick one rotten apple, we have [tex]^{7}C_1[/tex] ways in picking one rotten apple. But we still need to pick 2 more apples, and so, both of them have to be fine apples.
Hence, we have [tex]^{7}C_1 \cdot ^{21}C_2[/tex] ways in picking two good pples and one rotten apple, which is 1,470 different ways.
