Question

in a dog show there are 31 dogs competing in the terrier group the top three dogs will win a cash prize $500 and move on to compete for a place in the larger best in the show competition how many ways can the top three dogs be to determine if they're finishing position is not important

Answer 1

The total number of dogs area 31.

Determine the number of ways for determining top 3 dogs inspite of their position.

`\begin{gathered} ^(31)C_3=(31!)/(3!\cdot28!) \\ =(31\cdot30\cdot29)/(3\cdot2\cdot1) \\ =31\cdot5\cdot29 \\ =4495 \end{gathered}`

So there are 4495 ways for selceting top 3 dogs from