1. You will throw a fair coin 6 times, and will win on heads and lose on tails. Denoting a 'win' as a 1, and a loss as a '0', what is the probability of getting the following ordered sequence of wins and losses from a round of this game:
0,0,1,0,1,1
2. How many unique win/loss sequences produce a total of 3 wins out of 28 coin tosses?
3. What is the probability of getting exactly 4 heads out of 20 coin tosses?
4. 18 people are participating in a race. 4 trophies, for 1st through 4th place, will be given out. How many possible outcomes are there? (How many ways are there to allocate the 4 trophies among the participants?)
5. How many diagonals does a regular 11-sided polygon have?
6. A grocery store owner is trying to decide how to arrange his produce for the day. In one of the isles, he wants to put 5 different items: tomatos, zucchini, carrots, cantaloupes, and cucumbers. Since zucchini and cucumbers look so similar, he wants to avoid having them next to each other. How many different ways are there to arrange the isle, under this restriction?