gabrielle3laine gabrielle3laine
  • 03-01-2020
  • Mathematics
contestada

There are 12 men who may be elected to the council. If there are only 5 members of the council, how many different combination of council members are possible?

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frika
frika frika
  • 09-01-2020

Answer:

252 different combinations

Step-by-step explanation:

There are 12 men who may be elected to the council. If there are only 5 members of the council (the order doesn't matter), then there are

[tex]C^{10}_5\\ \\=\dfrac{10!}{5!(10-5)!}\\ \\=\dfrac{10!}{5!\cdot 5!}\\ \\=\dfrac{5!\cdot 6\cdot 7\cdot 8\cdot 9\cdot 10}{5!\cdot 5!}\\ \\=\dfrac{6\cdot 7\cdot 8\cdot 9\cdot10}{1\cdot 2\cdot 3\cdot 4\cdot 5}\\ \\=7\cdot 4\cdot 9\\ \\=252[/tex]

different combinations of council members.

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