Perhaps the brilliant minds here at the SDMB can help my friend. Her question is: if you are doing an activity that asks you to drag and drop 6 different phrases into 6 different slots, then how many possible combinations of right and wrong answers are there? She was thinking 21 (6+5+4+3+2+1), but someone else gave her the answer of 8. It’s been too long since I took finite math in high school, but 21 seemed like the right answer to me. I wanted to be sure though, so if anyone knows better, please help.
6! = 65432*1 = 720
The first phrase can go in any of 6 slots.
The next phrase can go in any of the remaining slots.
.
.
.
The last phrase has no choices, it must go in the only remaining slot.
I agree with muttrox, it is 720. The scary thing (for me) is that as soon as I saw the question, I knew the answer. Does anyone else have the factorials for below ten memorized for no good reason?
Thanks for the responses. I suspected that it might be a multiplication factorial rather than addition. I used to have the factorials memorized, but it’s been 10 years since I took finite math in OAC (in Ontario, we used to have a grade 13 in high school that was called OAC - Ontario Academic Credits or something like that).
Uh, not to be a party pooper, but nowhere in that question does it ask for all of the possible combinations of 1 to 6 not allowing for repetition.
It asks about phrases and right and wrong answers.
I think we need the actual question before it can be answered.
Here’s why I think this. If a phrase goes into a slot, and has the option in that slot of being either right, or wrong, then you have 2 possibilities for each of the 6 phrases per slot. Which makes 720 combos, but how do we know what the criteria for right and wrong are?
If one phrase in front of the other is a wrong answer, and the same phrase behind the other is a right answer, then you have 6 groups of 2 that can be calculated. That’s 15 combos per group, which makes 90 answers, and half are right, while half are wrong . OR if all of the phrases put together make one right answer, and each non-correct-as-far-as-order-goes phrase makes a wrong answer, you have 1 right answer and 5 wrong answers. Anyway, I think you get the point that I barely know what I’m talking about, and there’s not enough info provided, unless it’s just a poorly worded question that wants you to do a factorial. But I would maintain that 720 shouldn’t be the answer, since you are asking for a split between the possible combinations (ie right and wrong).
the end
I had assumed placing the correct phrase in the correct slot for all 6 phrases was a correct answer – anything else was a wrong answer. There are 720 ways to place the phrases in slots, so there would be 1 out of 720 ways to be right. Seeing as the person who posted the OP seems good with that, I think the assumption is safe. If the rules were more elaborate, I think they would have posted that in the OP.
Scule, care to comment?
If you’re allowed to repeat phrases, it’s 6[sup]6[/sup] = 46656
But I assume you’re not, so the 720 is probably right.
Assuming that putting the right phrase into the right slot counts as a right answer, and there is only one right phrase for each slot, and each phrase can only be used once:
There are 2 to the 6th possible ways to arrange right and wrong answers, but it is impossible to have only one wrong answer, that would necessarily make another answer wrong as well. So 2to the 6th = 64, and then you subtract the 6 possible ways to have one wrong answer, and you get 58 possible combinations of right and wrong answers.
I feel like a fool for doing this problem the hard way before realizing I could just subtract 6. Duh.
Like I said, it’s been quite some time since I took finite mathematics, but the basic gist is that there are 6 questions and 6 answers, and only one right answer for each question, so the other 5 are wrong for that question, and so on. That’s why the 720 seemed correct on reflection, because the number of possible combinations should be 6x5x4x3x2x1=720. However the number of correct combinations is only one, obviously, because there is only one combination where the answers will be placed all correctly (assuming you must get all 6 right to count as correct, we’ll ignore partial right and wrong answers). Hopefully that clears it up, and I am certainly not saying the 720 is definite, but it gels with what I remember from back in the day.