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?

1 Answer

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


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:


And so:

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