SOLUTION: Jace's collection of sports cards includes ten baseball, seven basketball, and nine football cards. He wants to give away two cards from different sports to his friend for a birthd

Algebra ->  Permutations -> SOLUTION: Jace's collection of sports cards includes ten baseball, seven basketball, and nine football cards. He wants to give away two cards from different sports to his friend for a birthd      Log On


   

Question 604911: Jace's collection of sports cards includes ten baseball, seven basketball, and nine football cards. He wants to give away two cards from different sports to his friend for a birthday present. How many ways can he choose the two cards?
I have tried 26P2 and 26C2 but I am not sure if any of these are right. I have also tried 26!/10!7!9!
I am not sure if I am working this problem out right. Please help my understand how this problem is worked out.
Thank you so much for your help!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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.