A marketing company is having an employee raffle to decide who gets to go on a day trip to the local amusement park. A group of 10 is to be chosen at random from a pool of qualified employees. There are 4 departments within this marketing company, of which, 4 employees are eligible for the raffle in Department A, 3 employees are eligible from department B, 5 employees are eligible from department C, and 7 employees eligible in department D.

1. What is the probability that both Jim and Dwight are selected, and each department has at least one member present in the group? (Jim and Dwight do not like each other)

2. At the amusement park, the group of 10 are waiting in line for the teacup ride. The ride consists of 5 differently colored teacups that can seat 2 people each. What is the probability that Jim and Dwight will sit in the same teacup together if everybody gets in the teacups at random?

3. Later that day, the group of 10 decide to sit down at a picnic table for lunch. Each side of the picnic table seats 5. If Dwight refuses to have Jim sit on other side of him, or in front of him, then how many ways can the group sit down at the picnic table? (Hint: Examine each case depending on where Dwight sits)