In how many ways can a team of 6 horses be selected out of a stud of 16, so that there shall always be three out of A B C A' B' C', but never A A' , B B' or C C' together

The number of ways is  10C3× number of ways of choosing out of ABC A'B'C', so that AA', BB' or CC' are not together         =10C3 (one from each of pairs AA′,BB′,CC′=10C3×8=10×9×81×2×3×8=960