SOLUTION: The dean of an Engineering School invites all 9 chairpersons and their spouses to his house for a Winter Solstice party. If each department chair may attend without a spouse, but

Algebra ->  Permutations -> SOLUTION: The dean of an Engineering School invites all 9 chairpersons and their spouses to his house for a Winter Solstice party. If each department chair may attend without a spouse, but       Log On


   

Question 492772: The dean of an Engineering School invites all 9 chairpersons and their spouses to his house for a Winter Solstice party. If each department chair may attend without a spouse, but the spouse may not attend without the department chair, how many different sets of attendees are possible?
[b] Think of another way to count the possible sets of attendees. If you can, also write the two approaches as a combinatorial identity.
Again I'm lost as to how to begin setting this problem up.
Answer by sudhanshu_kmr(1152) About Me  (Show Source):
You can put this solution on YOUR website!

Each chairperson can attend the party in 3 ways:
a) only chairperson
b) Chairperson and spouse
c) none of both.
total no. of ways = 3*3*...*3 = 3^9 = 19683