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Thank you for using the site. I'll be happy to help you with your math question.
I'm with you so far. Is there more to this problem? I'm not yet clear on what is being asked for.
Ok. For the purposes of your question does "draw a heart in the first five cards" mean any number of hearts drawn, or specifically one and only one heart?
Ok, thanks. I'll have a solution posted for you in a few minutes.
Here is the solution:
(Clicking on the above link will take you to a page where you can download the detailed solution as a Word document.)
Please feel free to ask if you have any questions about this solution. I'll be happy to explain anything that is not clear.