A committee is to be chosen from among 8 scientists, 7 psychics, and 12 clerics. If the committee is to have two members of different backgrounds, how many such committees are there?
There can be 3 โtypesโ of commitees:
The scientist + psychic commitee can be created in \(8 \cdot 7 = 56\) ways
The scientist + cleric commitee can be created in \(8 \cdot 12 = 96\) ways
The psychic +cleric commitee can be created in \(7 \cdot 12 = 84\) ways
The number of all possible commitees is the sum of the above:
\[8 \cdot 7 + 8 \cdot 12 + 7 \cdot 12 = 236\]