Question

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?

Answer 1

252 different combinations

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

`C^(10)_5\\ \\=(10!)/(5!(10-5)!)\\ \\=(10!)/(5!\cdot 5!)\\ \\=(5!\cdot 6\cdot 7\cdot 8\cdot 9\cdot 10)/(5!\cdot 5!)\\ \\=(6\cdot 7\cdot 8\cdot 9\cdot10)/(1\cdot 2\cdot 3\cdot 4\cdot 5)\\ \\=7\cdot 4\cdot 9\\ \\=252`

different combinations of council members.