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All Questions Answered Correctly Due At 9pm13. In a club with 21 members, how many ways can a slate of 3 officers consisting of president, vice-president, and secretary be chosen?14. Find the number of distinguishable permutations of the letters in the word “decreed”.15. A child has a set of differently shaped plastic objects. There are 5 pyramids, 3 cubes, and 6 spheres.a.) How many arrangements are possible if objects of the same shape must be grouped together and each object is a different color?b.) In how many distinguishable ways can the objects be arranged in a row if objects of the same shape are also the same color, but need not be grouped together?c.) In how many ways can you select 3 objects, one of each shape, if the order in which the objects are selected does not matter and each object is a different color?16. A committee of 12 members must forma sub-committee to present a paper.a.) How many ways can a 5 member sub-committee be formed if none are to be given special tasks?b.) How many ways can a 5 member sub-committee be formed if one member is to be the chair and another the recorder?c.) How many ways can a 5 member sub-committee be formed if the chair of the larger committee must be a member of the subcommittee?17. How many different 4-letter radio station call letters can be made ifa) the first letter must be K or W and no letter may be repeated?b.) repeats are allowed, but the first letter is K or W?c.) the first letter is K or W, there are no repeats, and the last letter is R?18. An automobile manufacturer produces 8 models, each available in 7 different exterior colors, with 4 different upholstery fabrics, and 5 interior colors. How many varieties of automobile are available?19. A group of 3 students is to be selected from a group of 14 students to take part in a class in cellbiology.a. In how many ways can this be done?b. In how many ways can the group who will not take part be chosen?20. A student randomly grabs 2 socks from a drawer containing 5 black, 7 brown, and 8 blue socks. What is the probability that he grabbed a matched pair? Write answer as a reduced fraction.21. A bank has 7 branches is Arkansas, 6 in Louisiana, and 10 in Texas. They have decided to close 3 of these branches. The branches to be closed will be chosen randomly.a.) In how many ways can they choose the 3 branches?b.) What is the probability they close 3 branches in Louisiana?c.) What is the probability they close at least 2 branches in Louisiana?d.) What is the probability they close 2 branches from the same state and the third from another?e.) What is the probability they close one branch from each of the three states?