Princeton Review
A city council will select 2 of 9 available firefighters and 1 of 6 available police officers to serve on an advisory panel. How many different groups of 3 could serve on the panel?
A. 36
B. 72
C. 144
D. 216
E. 432
OA D
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A city council will select 2 of 9 available firefighters and
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Global Stats
Ways to select 2 firefighters out of 9 is \(C^2_9=36\);
Ways to select 1 police officer out of 6 is \(C^1_6=6\);
Total ways to select 2 firefighters out of 9 and 1 police officer out of 6 is \(36 \cdot 6=216\).
It's called Principle of Multiplication: if one event can occur in \(m\) ways and a second can occur independently of the first in \(n\) ways, then the two events can occur in \(m \cdot n\) ways.
Ways to select 1 police officer out of 6 is \(C^1_6=6\);
Total ways to select 2 firefighters out of 9 and 1 police officer out of 6 is \(36 \cdot 6=216\).
It's called Principle of Multiplication: if one event can occur in \(m\) ways and a second can occur independently of the first in \(n\) ways, then the two events can occur in \(m \cdot n\) ways.
