Question

There are 16 members on a city council. At a recent city council meeting, 9 of the council members voted in favor of a budget increase. How many possible groups of council members could have voted in favor?

Will the calculation involve permutations or combinations?

• combinations
• permutations

There are ?  possible groups of 9 city council members who voted in favor of the budget increase

Answer 1

The order of the council members to vote in favor of a budget increase will not change the group of the members. That is to say, the order is not considered here

Therefore calculation involves combinations

There are $_{9}^{16}C$ possible groups $\{_{r}^nC=\frac{n!}{(n-r)!*r!}\}$

\implies _{9}^{16}C=\frac{16!}{(16-9)!*9!}=\frac{16!}{(7)!*9!}=11440

There are 11440 possible groups of 9 city council members who voted in favor of the budget increase