Combinatorics -- Bill Martin -- WPI

A Simple statement of Problem 10 on Assignment 1

In research, or working in a company, problems rarely come to us in a precise way. The statement of the problem is often ambiguous and the notion of a "solution" is open to debate.

Problem 10, as given on the assignment, is such a problem.

Here is a more precise version of the problem. Find all possible sequences of letters from the alphabet { D₁ , D₂ , A₁ , A₂ , A₃ , P } with the following properties:

the sequence must begin with D₁A₁ and D₁ appears nowhere else in the sequence;
the sequence must end with A₃ and A₃ appears nowhere else in the sequence;
there are exactly five appearances of P in the sequence;
A₂ appears at least once in the sequence;
each airport A_i is immediately preceded by at least one P.
D₂ appears only once, but is not the first, second or last symbol in the sequence.

HINT: Your list (which need not explicitly list every possible position for the D₂ symbol, but only count the number of such placements for each pattern) will have a total of 126 arrangements.