...then their analysis is flawed....

Careful, there, Studiot.

Let's see your analysis before you start suggesting that ours is flawed.

 

However, my approach insists that the characters are chosen in order of appearance and I come to the same conclusion! Hence, it looks like the order is unimportant, because anslysis using both methods produces identical results.

In my approach, I identify four independent scenarios and calculate the combinations for each of them. Then, summing those results and multiplying by 9x8 , I get the same answer as WBahn and joeyd99.

Your "fact" does not take into effect what a choice may have on future choices.

 

joey, do you think this

2. How many ways to choose 2 from a set of 24;

is a correct analysis in this situation

If however you insist that the characterers are chosen in order of appearance in the password then their analysis is flawed since there are 25 characters available at the instant of choice of the second character.

@djsfantasi

12 = 3*4
but it also equals
12 = 6*2

Two baskets, each containing 6 of a particular fruit, eg 6 apples and 6 pears

is not the same as

3 baskets each containing 4 of a particular fruit, eg 4 apples, 4 pears and 4 bananas

although the total number of items of fruit is the same in both cases.

 

joey, do you think this...

...is a correct analysis in this situation

I know it is. But the onus is on you now to prove it's not.

I assert 794,880 solutions to the problem.
You assert 397,440.

All you need to do is show 1 of 397,440 solutions is incorrect. Go for it.

 

So , joey, you are avoiding my question.

I don't have to prove anything.

I posted a problem for discussion, and have asserted very little since there is possibly an issue with the original text.

I certainly do not assert that the solution is 397,440.

However you have asserted that there are only 24 possible choices for the second letter, so prove it.

 

I don't have to prove anything....

I ... have asserted very little ...

Sorry, joeyd, but No.

I consider "No" an assertion.

 

So , joey, you are avoiding my question.

I am not avoiding it. I believe your question has been answered in many different ways, by three different people.

So far, WBahn's analysis has been the most rigorous, showing both a solid mathematical analysis backed up by a computer simulation that solves the problem in precisely the order you originally stated.

I don't have to prove anything.

You posed the question. You claimed to know the answer (by outright rejection of mine). You promised an answer "tomorrow". Your answer has yet to be forthcoming. Instead you appeal to authority claiming that you must be correct because a third party (the exam board) is very, very, rarely wrong.

This is math, not AGW. Consensus doesn't work here (nor should it in AGW, but that is besides the point).

I think your credibility is at stake with respect to this problem. Using your own mind, you need to either:

a) Accept our analysis and solution is correct;
b) Reject our analysis and posit your own, along with evidence supporting your position.

 

I'm not changing the rules of the original problem. I'm creating a set of rules that are consistent with the solution claimed by studiot as one more way of showing that the claimed solution does NOT agree with the original rules.

 

I understand WBahn's answer and note that joey's working is equivalent,

But I also note that there is a question as to how the password is to be formed.

If you allow the selection of the second vowel before the first consonant WBahn and joey are correct.

If however you insist that the characterers are chosen in order of appearance in the password then their analysis is flawed since there are 25 characters available at the instant of choice of the second character.
This fact is not reflected in joey's permutation expression.

And yes, I have played with a few smaller models to see how things work out, but I am reserving judgement until I have the full information

My solution is NOT dependent on selecting the second vowel before the first consonant. I explicitly enumerated the possible paths in Post #9 and even more explicitly in Post #29. I fully enumerated toy examples in Posts #33 and again in Post #45. I presented a script that fully enumerates the actual problem choosing the characters in order in Post #39. I've offered to upload a file containing all 794,880 legal passwords so that anyone can comb through it and prove it incorrect by doing any one of three things: (1) finding a single entry that is not a legal password, (2) finding a single legal password that is not in the file, or (3) finding a single example of a duplicate entry. I even said that I am willing to put money on the line at 10:1 odds. Why are you ignoring all of these and continue to claim that my solution requires the selection of the second vowel before the first consonant?

As I said in earlier posts -- back up this oft-repeated claim that order counts by showing how my claim that order doesn't matter when computing the number of legal combinations by stating the "correct" way to compute the number of combinations in Post #45 and then showing how my "incorrect" answer of 36 is wrong by fully enumerating the correct set of passwords and showing that it is different that the set of 36 I enumerated.

 

And I have shown that there is a 1:1 correspondence of the solution sets between the rules:

VLLV

and

VVLL

by simply transposing the 2nd and 4th character positions for each permutation of the VLLV solution set.

 

So , joey, you are avoiding my question.

I don't have to prove anything.

I posted a problem for discussion, and have asserted very little since there is possibly an issue with the original text.

I certainly do not assert that the solution is 397,440.

However you have asserted that there are only 24 possible choices for the second letter, so prove it.

Forget about the question of whether the problem YOU posted HERE is the same as the original problem posted in some exam review book somewhere. What do YOU claim the correct solution is for the problem YOU posted HERE?

How can you keep saying that our solutions are flawed but yet be unwilling to post a "correct" solution?

Joeyd999 is NOT asserting that there are only 24 possible choices for the second letter, he is merely asserting that the total number of possible legal combinations is that same as if there were.

 

...answer tomorrow.

We are nearing the end of the 2nd day after "tomorrow" and, still, no official answer from the great and powerful messenger of the exam board.

 

I'm waiting! Of course, there may be some difficulty in telling the difference between tomorrow and three days later.

What I don't understand is why studiot can't show us a solution, particularly as he was advising the OP in another forum. Please explain this to us.

My approach, while not as detailed as WBahn's, was extensive. I detailed the various combinations depending on different scenarios. And I come up with the same answer as WBahn and joeyd99. So with three approaches producing the same answer, show us our mistake.

 

What I don't understand is why studiot can't show us a solution

I have already said that I have come to the conclusion there must be more to the question that was originally posted and that I am trying to obtain the actual wording of the original to post here.

 

I have already said that I have come to the conclusion there must be more to the question that was originally posted and that I am trying to obtain the actual wording of the original to post here.

But it doesn't matter what the original question that was posted somewhere else was! You posted a question HERE and it is THAT question that was asked and it is THAT question that was answered.

 

You posted a question HERE and it is THAT question that was asked and it is THAT question that was answered.

Yes it was and It have already said that way back

If you allow the selection of the second vowel before the first consonant WBahn and joey are correct.

Actually, looking back I note from your post#8 that you also did a more complete analysis, allowing for the conditional situations.

joey also said

My answer is correct, or you mis-described the problem.

and I am actively pursuing that possibility at the moment.

I don't see any cause for anyone to get so hot under joey's hat, I'm sure we will all be able to agree on a solution and what went wrong when all the information is collected.

 

...I'm sure we will all be able to agree on a solution and what went wrong when all the information is collected.

What are you, some kind of politician?

Nothing went "wrong". You posted a question. I posted an answer. You said it was wrong.

What is your answer?

 

Joey and WBahn, you have an error in the fourth place.

...And yes order does matter...

...If however you insist that the characterers are chosen in order of appearance in the password then their analysis is flawed since there are 25 characters available at the instant of choice of the second character.

These affirmative comments were made by you, not the "exam board". Please support them with proper arguments.

 

I'm waiting! Of course, there may be some difficulty in telling the difference between tomorrow and three days later...

Has there ever been a rigorous scientific study to determine when "tomorrow" becomes "today"?

If not, the day Studiot gives us an answer may provide a clue. I think a paper is in order. Journals will publish anything these days.

 

My answer is correct, or you mis-described the problem.

...and I am actively pursuing that possibility at the moment.

Completely irrelevant!

The problem you stated is the only problem you were aware of -- and the only problem for which you were providing your assertions!

This is starting to feel like the arguments I have with my wife. She asks a question for which she thinks she knows the answer, and then argues that I must be wrong because I answered the wrong question.

Fortunately, I like to argue.