a) The 10 members of the committee have to choose one presidentand two vice presidents (these have to be three different people).In how many ways can they choose these officers? (Note: here is nodistinction between the two vice presidents; there is not a “first”VP and a “second” VP).
b) Three couples go to a movie theater. They sit in consecutiveseats such that each couple is seating together, that is eachperson is seating next to his/her partner. If there are 6 seatsavailable, in how many ways can they sit?
c) A university wants to assign a three digit number to eachclassroom of a new building. They can use the digits {1,2,3,4,5}but they cannot use any digit more than once. How many classroomnumbers can they assign if the numbers have to be less than250?
d) The University wants to select 4 students for a feedbacksurvey. They want all four students from either Prof. X’s sectionor Prof. Y’s section. Prof. X has 40 students in his class andProf. Y has 30 students in his class. How many selections arepossible?
