6. The bowling club has 37 members. a. They need to elect a slate of ofﬁcers including a president, vice president, recordingsecretary, corresponding secretary, treasurer, historian, and statistician. If each ofthemembers can be elected to any of the positions and each member may only hold oneposition, how many different slates of ofﬁcers can be elected? b. They need to select seven members to serve on the executive committee. How manydifferent executive committees can be chosen? 7. Six friends decide to visit Larry’s Lunchwagon for lunch. On today’s menu, Larry has eightdifferent varieties of plate lunches.a. If each of the friends orders a diﬁerent type of plate lunch to eat, how many different waysare there to choose six different plate lunches assuming that order of choice does notmatter? b. If each of the friends orders a plate lunch to eat and two or more of them might order the some type of lunch, how many different ways are there to choose six plate lunches assumingthat order of choice does not matter? 8. Find the number of permutations of the word: AUMAKUA. 9. Suppose an urn contains 3 red balls, 6 green balls and 2 blue balls. What is the probability thata ball drawn at random from the urn is blue? 10. Suppose a card is drawn at random from a standard 52—card poker deck. What is the probabilitythat the card is black or has a face (jack, queen or king}?