  We apply the method of characteristics for the solution of pde's to two
combinatorial problems. The first is finding an explicit form for a
distribution that arises in bio-informatics. The second is a question raised by
Graham, Knuth and Patashnik abiout a sequence of generalized binomial
coefficients. We find an exact formula, which factors in an interesting way, in
the case where one of the six parameters of the problem vanishes. We also show
that the associated polynomial sequence has real zeros only, provided that one
parameter vanishes, and the other five are nonnegative.
