Question

A town is forming a committee to investigate ways to improve public safety in the town. The committee will consist of three representatives from the seven​-member town​ council, two members of a six​-person citizens advisory​ board, and three of the 10 police officers on the force. How many ways can that committee be​ formed?

Answer 1

Answer:

63,000

Step-by-step explanation:

Three representatives from the seven​-member town​ council can be chosen in

$C^7_3=\dfrac{7!}{3!(7-3)!}=\dfrac{7!}{3!\cdot 4!}=\dfrac{4!\cdot 5\cdot 6\cdot 7}{2\cdot 3\cdot 4!}=5\cdot 7=35$

different ways.

Two members of a six​-person citizens advisory​ board can be chosen in

$C^6_2=\dfrac{6!}{2!(6-2)!}=\dfrac{6!}{2!\cdot 4!}=\dfrac{4!\cdot 5\cdot 6}{2\cdot 4!}=5\cdot 3=15$

different ways.

Three of the 10 police officers on the force can be chosen in

$C^{10}_3=\dfrac{10!}{3!(10-3)!}=\dfrac{10!}{3!\cdot 7!}=\dfrac{7!\cdot 8\cdot 9\cdot 10}{2\cdot 3\cdot 7!}=4\cdot 3\cdot 10=120$

different ways.

In total,

$35\cdot 15\cdot 120=63,000$

different ways to form the committee