Question

There are 11 horses in a race. In how many ways can the first three positions of the order of the finish occur? (Assume there are no ties.)A. 990B. 163C. 165ООD. 994

Answer 1

Find the position of the order of the horse race:

Total number of horse = 11

The position of order are first , second and third = 3

`^(11)C_{^{}3}`
`\begin{gathered} ^(11)C_{^{}3}=(11!)/((11-3)!3!) \\ ^(11)C_{^{}3}=(11!)/(8!3!)=\frac{11\text{ x 10 x 9 x 8!}}{8!\text{ 3 x 2 x }1} \\ \text{ }^(11)C_{^{}3}=\text{ 165} \end{gathered}`

Therefore the number of ways first three poisition will occur = 165

Hence the correct answer is Option C