1. In a completely dark room with ten chairs, six people come and occupy six chairs at random. What is the probability that at least one of three specific chairs gets occupied?

2. A group of six men and 12 women are partitioned into six committees of three people each. What is the probability that each committee contains a male member?

3. * (The General Shoes Problem). There are n pairs of shoes of n distinct colors in a closet and 2m are pulled out at random from the 2n shoes. What is the probability that there is at least one complete pair among the shoes pulled?

4. Find the probability that, after n rolls of a fair die, the sum of the rolls will be no less than 6n- 1.

5. * (Clever Counting). n balls from a total of N balls, labeled as 1; 2; ··· ;N , are taken out from an urn and the label of each written down. Find the probability that the labels form an increasing sequence.

Hint: See the text for a similar example.