[a] The dean of an Engineering School invites all 9 department chairpersons and

Question

[a] The dean of an Engineering School invites all 9 department 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? (The dean and dean’s spouse will both be attendees in every case.) [b] Think of another way to count the possible sets of attendees. If you can, also write the two approaches as a combinatorial identity, valid for any positive integer n as the number of department chairs. Hint: The hard approach uses combinations.

Only need part B

Explanation / Answer

Each chairperson can attend the party in 3 ways:
a) only chairperson

B)i)Chairperson and spouse
ii)none of both.
total no. of ways = 3*3*...*3 = 3^9 = 19683

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