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The mascot of High Tech High is Wendell the Wizard. For the homecoming football game, the cheerleaders have made seven large cards that together spell out “WIZARDS.” Each card has one letter on it, and each cheerleader is supposed to hold up one card. At the end of the first quarter, they realize that someone has mixed up the cards.  

  1. How many ways are there to arrange the cards?

    Try using a factorial to represent the different arrangements.

  2. If they had not noticed the mix up, what would be the probability that the cards would have correctly spelled out “WIZARDS”?