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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 :

The total number of dogs area 31.

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

[tex]\begin{gathered} ^{31}C_3=\frac{31!}{3!\cdot28!} \\ =\frac{31\cdot30\cdot29}{3\cdot2\cdot1} \\ =31\cdot5\cdot29 \\ =4495 \end{gathered}[/tex]

So there are 4495 ways for selceting top 3 dogs from

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