P&C q5

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Saumyojit

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The results of 21 football matches (win, lose,draw) are to be predicted. The no. of different forecasts that can contain 18 correct results is


Each football match has three options of results.
So 21 matches has 63 options for results

Now, different forecast this line .....
This means that each forecast has predicted result for each 21 matches and it happens to be that each forecast's prediction contains 18 correct and 3 wrong .

It CANNOT happen that one of the forecast has predicted 17 correct or 20 correct .... that is not my required .

Now also I don't know how many forecasts are there in total .


What is the meaning of Different forecasts ?

Suppose one forecast is predicted by one person and another forecast is another person like this?

Or every forecasts shall have 18 results predicted in each *Unique* combinations .

Forecast 1 has 18 th match , 20 th match as win .

Whereas forecast 2 predictions are same as 1 except 18 th match and 20th match as loss ( so in two matches they beg to differ).

If so,

18 results means 18 matches; we need to consider any 18 different matches out of 21 .


21C18 this gives us all possible unique combination of 18 matches which translates to each new 18 correct results predictions of each different forecast ?
 
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Saumyojit said:
The results of 21 football matches (win, lose,draw) are to be predicted. The no. of different forecasts that can contain 18 correct results is
Click to expand...
What you've written is almost incomprehensible. I'll boil it down to one issue.

You ask what "different forecasts" means. Let's take a smaller example.

If there were 3 matches, then there are 3^3 = 27 possible forecasts:

WWW, WWL, WWD, WLW, WLL, WLD, WDW, WDL, WDD,
LWW, LWL, LWD, LLW, LLL, LLD, LDW, LDL, LDD,
DWW, DWL, DWD, DLW, DLL, DLD, DDW, DDL, DDD

If the actual outcome is DWW, then these would have 2 correct results:

WWW,
LWW,
DWL, DWD, DLW, DDW

How can these be counted? Hint: one way is to consider which ones are wrong, and then what wrong predictions were made.
 
Dr.Peterson said:
What you've written is almost incomprehensible
Click to expand...

Okay i have edited a bit

The results of 21 football matches (win, lose,draw) are to be predicted. The no. of different forecasts that can contain 18 correct results is


⁠Each football match has three options of results.
⁠So 21 matches has 63 options for results





⁠Now I know 63 forecasts are there in total .
 
Saumyojit said:
The results of 21 football matches (win, lose,draw) are to be predicted. The no. of different forecasts that can contain 18 correct results is
Click to expand...
This is an incomplete sentence. Are we to fill in a blank at the end? Say so, so the reader doesn't expect the next line to continue it. And is this the entire problem, exactly as given to you? Where is it from?

Saumyojit said:
Each football match has three options of results.
⁠So 21 matches has 63 options for results
Click to expand...
Why would you multiply the number of matches by the number of options for each? I hoped my example would show you that this is wrong. (In my example, you would be saying there are 3*3 = 9 possible results, but I listed more than that.)

When you ask for help, pay attention to what you are told.
 
Dr.Peterson said:
f there were 3 matches, then there are 3^3 = 27 possible forecasts:

WWW, WWL, WWD, WLW, WLL, WLD, WDW, WDL, WDD,
LWW, LWL, LWD, LLW, LLL, LLD, LDW, LDL, LDD,
DWW, DWL, DWD, DLW, DLL, DLD, DDW, DDL, DDD
Click to expand...
Each match has 3 possibilities.
if 21 matches have been played then there would be 3^21 possible forecasts.
Sorry.

Dr.Peterson said:
And is this the entire problem, exactly as given to you?
Click to expand...
yes.

Dr.Peterson said:
f the actual outcome is DWW, then these would have 2 correct results:

WWW,
LWW,
DWL, DWD, DLW, DDW
Click to expand...
Now I understood what the question means .

Out of 3^21, i have to find those combinations which have 18 correct results which matches the actual Outcome

Outcome:
Results : w w ww wwwww w w w w w d d d d d d d
Matches: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Now some of the combinations must have any 18 right Results from any 21 matches.

All this time I didn't understood what was being asked.

THanks .
I will solve it tommorow after 7 hrs .
 
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Saumyojit said:
Outcome:
Results : w w ww wwwww w w w w w d d d d d d d
Matches: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Now some of the combinations must have any 18 right Results from any 21 matches.
Click to expand...
I'm not sure what the table means, but I'll restate what I think this sentence means:

You need to count all the possible lists of 21 predictions in which exactly 18 of them are correct (that is, match some specified but unknown list).​

(This is just my interpretation, and there are a couple points at which I could be wrong. But this is what makes most sense to me. I n particular, I am unhappy with the wording "that can contain 18 correct results". I'm not sure this was written by a native English speaker.)
 
Some things that I found out ,

We need to subtract forecast which doesn't have 18 correct results from 3^21.

How to count the wrong forecasts

How will I know the forecasts that have either less than 18 correct results or greater than 18 .



Suppose I have fixed in my mind that any 18 results are correct and three are wrong

So choosing 3 matches where the results have not matched out of 21(and the rest 18 is correct) will do the work?

21C3 =1330=21c18

Why this is WRONG?
 
Saumyojit said:
We need to subtract forecast which doesn't have 18 correct results from 3^21.

How to count the wrong forecasts

How will I know the forecasts that have either less than 18 correct results or greater than 18 .
Click to expand...
I would not try subtraction, for exactly this reason: I don't see how to do it. You try different ideas, and use those that work, not those that don't (though sometimes you find you have to come back to a rejected idea).

But we aren't trying to count wrong forecasts! We're trying to count forecasts with exactly three wrong.

Saumyojit said:
Suppose I have fixed in my mind that any 18 results are correct and three are wrong

So choosing 3 matches where the results have not matched out of 21(and the rest 18 is correct) will do the work?

21C3 =1330=21c18

Why this is WRONG?
Click to expand...
This doesn't take into account that there are two ways to be wrong on a given match! If the match is a W, you'll be wrong if you say L or D. Look at post #2, where I gave you everything you needed.

But how do you know you're wrong? Once again, you apparently have a "correct" answer but have not told us what it is, though we've told you repeatedly to give us everything you have. As we said, if the answer you were given is wrong, we'll waste time trying to help you if your answer is really right but you think you're wrong.

By ignoring what we tell you, you are showing great disrespect, and risking being banned.
 
Dr.Peterson said:
This doesn't take into account that there are two ways to be wrong on a given match!
Click to expand...
Ok now I understood
Three matches that will be Selected every time to have WRONG predictions ; each one of them have two options of Result other than the original outcome .
2^3


First select3 matches to have WRONG predictions, 21c3, then 21c3 * 2^3
 
Dr.Peterson said:
But how do you know you're wrong? Once again, you apparently have a "correct" answer but have not told us what it is,
Click to expand...
@Saumyojit - You still did not tell us what the "given" correct answer is (against which you are comparing your trial answers). Please tell us through your next post - otherwise the ban hammer is going to come down.
 
Interestingly, all the pages I found containing your first sentence had 19 rather than 18 in the second sentence. And at least one of them gave a numerical answer, not an expression like yours. Nothing except your question has 18. So you can't argue that we could have found your problem by searching, and didn't need you to tell us everything. As far as I could tell, you modified the question yourself and did not have an answer to compare with.

Please, again, in the future don't leave us to guess.
 
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