How many unique arrangements can be made of 6 people who have to sit in 6 chairs, while leaving three chairs empty, and three people unseated. The order of the unseated does not matter.
Two logical way:
1) how many ways can you pick three people out of six? For each of those ways, how many ways can you assign a seat number to each person?
2) how many ways can you pick the three chairs that will be occupied? Given those chairs, how many ways can you fill them with six people?
You should get the same answer both ways....
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993