Question

There are 10 students in a classroom, including the triplets Hugh, Stu, and Lou. If 3 of the 10 are randomly selected to give speeches, what is the probability that Hugh will be first, Stu will be second and Lou will be third?

Answer 1

`P("Hugh first, Stu second, Lou third")=1/720~=.0014`

Explanation:

This question is asking about permutations - randomly picking elements from a population where the order of the picks matters. The general formula is:

`P_(n,k)=(n!)/((n-k)!); n="population", k="picks"`

We are interested in permutation involving having Hugh be first, Stu second, and Lou third. There is only 1 permutation where that can happen.

There are a total of `P_(10,3)` permutations that can be made:

`P_(10,3)=(10!)/((10-3)!)=(10!)/(7!)=(10xx9xx8xx7!)/(7!)=10xx9xx8=720`

And so:

`P("Hugh first, Stu second, Lou third")=1/720~=.0014`