The task is to find the # of arrangements of six 0's, five 1's and four 2's with the restriction that the first 0 precedes the second 1.
I have worked it out by finding total # of arrangements (630630), and subtracting invalid arrangements
(i) firstly arranging 11 followed by the remaining 1's & 0's
(ii) fitting the 2's into the "interstices" in various patterns
I get a (hopefully correct) answer of 515970, but the process seems crude, and the question is:
Is there some slicker way of solving it ?