Question 1: Permutations and combinations (30 points) Robatic club at AUM has 20 members, divided into three classes: 7

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Question 1: Permutations and combinations (30points)
Robatic club at AUM has 20 members, divided into three classes:7 are seniors, 4 are juniors, and 9 are sophomores.
a. In how many ways can the club select a president, a secretaryand a treasurer if every member is eligible for each position andno member can hold two positions? [Show your work]
b. In how many ways can the club choose a group of 3 members toattend the next conference in Washington? [Show your work]
c. In how many ways can the club choose a group ofsix members to attend the conference in Washingtonif there must be two members from each class? [Show your work]
Question 2: Conditional probability, Bayes' theorem (30points)
Consider anelectronics repair shop with 4 different services. Suppose that 70%of the devices will need service 1, 10% of the devices will needservice 3, and 5% of the devices will need service 4. Of thedevices that will need service 1, 10% will have an extra charge, ofthe c devices that will need service 2, 1.5% will have an extracharge, of the devices that will need service 3, 99% will not havean extra charge, and of the devices that will need service 4, 98%will not have an extra charge
a) What is theprobability that a randomly selected device will have an extracharge? [10 points]
b) If we know that arandomly selected device will have an extra charge, what is theprobability that the devices will need service 3? [10 points]
Please solvethem all, i'm in urgent need for thier solution, i fear that idon't have extra question to post it again. and please don'tmention answers policy
i willupvote, if they all solved for sure