cramya wrote:Ron,
Could you please point me to what I am missing in my arrangements/approach?
Regards,
Cramya
you've basically made the same single mistake several times. here's the basic idea:
if you're going to multiply possibilities, then those numbers of possibilities have to be independent of one another (i.e., the numbers have to work out the same way regardless of who is chosen).
here's one place where you ran afoul of that principle:
Tom in 1 Jerry in 2 Donaled not in 4th
T J 4 2 2 1 =16
wrong.
you can say there are four choices for the third spot, but then you run into trouble:
you don't know how many choices there are for the fourth spot.
here's the problem:
if you happened to pick donald for the 3rd spot, then there will be 3 choices for the 4th spot (everyone who's left; no need to worry about donald anymore). on the other hand,
if you pick anyone but donald for the 3rd spot, then the numbers are 2, 2, 1, as you wrote.
this was articulated by stop800 in one of the above posts.
--
here's further proof that this method is not working:
Tom in 1 Donald in 4th and Jerry not in 2nd
T 3 3 D 2 1 = 18
now
this is actually a correct answer, because (by accident, it seems) you're
choosing the restricted slot (i.e., the second slot)
first.
but the reason you should notice there's a problem is that you have two IDENTICAL situations - two people in fixed locations, a third person with one prohibited location, and three people who can go anywhere - and yet you get two different numbers of possibilities (16 vs. 18). this is of course impossible: if you present two exactly identical situations, you have to get the same number of possibilities both times.
this observation won't tell you what to do to
fix the problem, nor will it even diagnose the problem, but at least it's a symptom.
--
by the way, you can fix the '16' above by picking the 4th slot (the restricted one) first:
t j 3(chosen second) 3(chosen first) 2 1 = 18.
