In order to make a number greater than 500, the first digit drawn must be 5, 6, or 7. That is, it must be one of three specific digits. The next number drawn will be any of the 6 remaining cards, and the final number drawn will be any of the 5 remaining cards. In total, there will be 3*6*5 =

**90 ways**to draw the cards so that a number greater than 500 will result.