Question

in a dog show there are 31 dogs competing in the terror group the top three dogs with we'll all wind crash price of $500 and moved on to complete for a place in the larger Best in Show competition how many ways can the top three dogs be determined if they are finishing position is not important

Answer 1

The selection of three dogs out of 31 dogs can be done in

`31C3\text{ ways}`

i.e.

`\begin{gathered} =(31!)/((31-3)!*3!) \\ =(31*29*28!)/(28!*3!) \\ =(31*29)/(6) \\ =149.8 \\ \cong\text{ 150} \end{gathered}`