Following Problem -

A marketing company ls haying 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 ln Department A, 3 employees are eligible from department B, 5 employees are eligible from department C, and 1 employees eligible in department D. a.] How many ways can a group of to be selected from eligible employees? b.) what is the probability that at least one person from each department is selected? c.) Two employees from department D, Jim and Dwight, do not like each other. How many ways are there to select a group of 10 in which Dwight and Jim are not both selected? d.) What is the probability that both Jim and Dwight are selected, and each department has at least one member present in the group?e.]I 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 lfeyeryhody gets in the teacups at random? f.) 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 en where Dwight sits)