Answer:
672
Step-by-step explanation:
If there must be at least 4 people in each group, then the number of people in the group for tennis must be 4, 5, or 6.
There are
(10/k)=(10!)/(k!(10−k)!)
ways of choosing k people from a group of 10, and so there are
(10/4)+(10/5)+(10/6)=(10!)/(4!6!)+(10!)/(5!5!)+(10!)/(6!4!)
=2×(10×9×8×7)/(4×3×2×1)+(10×9×8×7×6)/(5×4×3×2×1)
=2×(10×3×1×7)/(1×1×1×1)+(1×3×2×7×6)/(1×1×1×1×1) =420+252=672
