Question

there are 11 members on a city council at a recent city council meeting, 4 of the council members voted in favor of a budget increase. how many possible groups of council members could have voted in favor

Answer 1

We have 11 members at the city council meeting, 4 voted in favour of a budget increase.

The possible groups of council members who could have voted in favour can be found using the combination formula which is used when we want to group items, in this case, we are grouping people.

Here is the formula;

Where n = Total members on the city council = 11

and r = members that voted in favour = 4

We will then solve this to be

$\begin{gathered} \frac{11!}{(11-4)!4!} \\ =\frac{11\times10\times9\times8\times7!}{7!\times4\times3\times2\times1} \\ =11\times10\times3 \\ =330 \end{gathered}$

This implies that there are 330 possible groups of council members who could have voted in favour.

ANSWER: 330