Counting

1. The "Pile High Deli" offers a "simple sandwich" consisting of your choice of one of five different kinds of bread with your choice of butter or mayonnaise or no spread, one of three different kinds of meat, and one of three different kinds of cheese, with the meat and cheese "piled high" on the bread. In how many ways may you choose a simple sandwich?
2. In how many ways may a class of twenty students choose a group of three students from among themselves to go to the professor and explain that the three-hour labs are taking ten hours?
3. A basketball team has 12 players. However, only five players play at any given time during a game. In how many ways may the coach choose the five players? To be more realistic, the five players playing a game normally consist of two guards, two forwards, and one center. If there are five guards, four forwards, and three centers on the team, in how many ways can the coach choose two guards, two forwards, and one center? (optional) What if one of the centers is equally skilled at playing forward?
4. What is the 7^th term of the expansion of (3a⁴+5b⁶)¹⁰?