Question

Four accounting majors, two economics majors, and three marketing majors have interviewed for five different managerial positions with a large company. Find the number of different ways that five of these people could be hired if the first two positions are to be filled by an accounting manager and an assistant accounting manager, the third position is to be filled by an economics manager, and the last two positions are to be filled by a marketing manager and an assistant marketing manager.

Answer 1

Let our four accounting majors be A, B, C, and D; our two economics majors be E and F; and our three marketing majors be G, H, and J, as follows:

ABCD EF GHJ

These are the possible arrangements:

ABEGH, ABEGJ, ABEHJ, ABFGH, ABFGJ, ABFHJ, ACEGH, ACEGJ, ACEHJ, ACFGH, ACFGJ, ACFHJ, ADEGH, ADEGJ, ADEHJ, ADFGH, ADFGJ, ADFHJ, BCEGH, BCEGJ, BCEHJ, BCFGH, BCFGJ, BCFHJ, BDEGH, BDEGJ, BDEHJ, BDFGH, BDFGJ, BDFHJ, CDEGH, CDEGJ, CDEHJ, CDFGH, CDFGJ, CDFHJ

There are thirty-six possible arrangements.