1.

A password consists of 5 characters. The first character must be a letter chosen from the English alphabet, one of the remaining 4 characters must be a digit chosen from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, and each of the remaining 3 characters must be a special character from the set {!, @, #, $, %, &}. How many different passwords are possible?

5.

8 members from the math department, 8 members from the biology department, and 8 members from the English department have declared themselves candidates for two vacant faculty senate seats. Suppose the two seats cannot be filled by two members from the same department, in how many ways can the two seats be filled?

7.

Emma has 14 different teddy bears. In how many ways can she name one bear the President, one the Vice President, one the Speaker of the Den, and 3 Senior Advisors to the President?

8.

Suppose there are 14 people in a room, how many handshakes will be done if each person shakes hands with every other person exactly once?

9.

There are 36 numbered balls in a drum (think lottery). A robot randomly picks 6 balls, I also randomly pick 6 balls. In how many ways can 4 of the balls picked by me be among the 6 balls picked by the robot?