Consult the Technology Guide to see how to enter the factorial operation on the calculator. In some counting situations, order makes a difference. For example, if we arrange people into a line (first...

Consult the Technology Guide to see how to enter the factorial operation on the calculator. In some counting situations, order makes a difference. For example, if we arrange people into a line (first to last), then each different ordering is considered a different arrangement. The number of ways in which you can arrange n individuals in a line is n!.

a. In how many ways can you arrange 5 people in a line?

b. How many people will result in more than 1000 possible arrangements for a line?

 c. Suppose you remember that your four-digit bank card PIN number uses 7, 5, 3, and 1, but you can’t remember in which order they come. How many guesses would you need to ensure that you got the right PIN number?

 d. There are 52 cards in an ordinary deck of playing cards. How many possible shufflings are there of a deck of cards?