[tex]\begin{gathered} \text{When we have a group of "n" elements, and we want to count how many groups} \\ \text{ of "k" elements we can form from the initial group, we use the combinatory formula:} \\ nCk=\frac{n!}{k!(n-k)!} \\ \\ \text{where }n!=1\cdot2\cdot\ldots\cdot n \\ \\ \text{for example; if n=4,} \\ 4!=1\cdot2\cdot3\cdot4=24 \end{gathered}[/tex][tex]\begin{gathered} \text{The groups of seven dogs that can be selected grom a group of 14 is} \\ 14C7=\frac{14!}{7!(14-7)!}=\frac{87178291200}{5040\cdot\text{ }5040} \\ =\frac{87178291200}{25401600}=3432 \\ \\ \text{Thus, there are 3432 ways to make groups of seven dogs from a group of 14} \end{gathered}[/tex][tex]undefined[/tex]
