Question 604911
Use the counting principle. 



Say the two cards are a baseball and a basketball card. So there are 10*7 = 70 ways to give these two cards out.


OR


Say the two cards are a baseball and a football card. So there are 10*9 = 90 ways to give these two cards out.


OR


Say the two cards are a basketball and a football card. So there are 7*9 = 63 ways to give these two cards out.



Now add up the number of ways: 70+90+63 = 223



So there are 223 ways to hand out 2 cards where the cards are from different sports.