1) How many distinct ways can you arrange the letters in the word: EXTREME

 

2) How many ways can 3 different prizes of $500, $300, and $50 be awarded if there are 30 people in the running for the prizes?

 

3) How many distinct groups of 5 people can be made from 12 people?

 

4) In a certain state, the Mega Millions Lottery has 2 separate pools of balls, each containing 57 balls.  How many possible arrangements of 5 balls from the first pool and 1 Mega ball from the second pool exist?