SOLUTION: a large sack contains six basketballs and five volleyballs. Find the number of ways that four balls can be selected from the sack if you must select at least two volleyballs?

Question 1201256: a large sack contains six basketballs and five volleyballs. Find the number of ways that four balls can be selected from the sack if you must select at least two volleyballs?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

We can select...
2 of the 5 volleyballs AND 2 of the 6 basketballs, OR
3 of the 5 volleyballs AND 1 of the 6 basketballs, OR
4 of the 5 volleyballs AND 0 of the 6 basketballs

By basic principles of combinatorics, "AND" means multiply and "OR" means add. So the number of ways we can select at least 2 volleyballs is

C(5,2)*C(6,2) + C(5,3)*C(6,1) + C(5,4)*C(6,0) = (10)(15) + (10)(6) + (5)(1) = 150 + 60 + 5 = 215

ANSWER: 215

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