Few questions about modal auxiliaries

[Dany]

Dear all,

I need help again in the usage of modal auxiliaries.

Can or could
Till now I have chosen it only on a gut level, and I thought that it I was right.
But now, after I have read about the usage of them, I'm really confused . Please help me.

I've read the following:
Can is used when you demonstrate an theoretical possibility.
Example: It can be very hot in September.

Could is used when you demonstrate a present possibility.
Example: It could be very hot in September, so take some summer clothes.

I have made an exercise about modal auxiliaries. In this exercise I should rephrase the given sentence via modal auxiliary without changing the meaning. Here is one example of the exercise:
It is often very crowded in discotheques.
I have rephrased this sentence like this:
It could be very crowded in discotheques.
The books' answer is:
It can be very crowded in discotheques.
Before I have read the above mentioned explanation, I had also chosen "can". But after reading it, I don't understand why "could" is wrong here.

Should, ought to or must
He ought to be at home now.
Can I use "must" indeed of "ought to" without changing the meaning?
He should be at home now.
Can I use "ought to" indeed of "should" without changing the meaning?

Please give me some explanations of the right answers in refer to my mistakes.
In this exercise I should rephrase the given sentence via modal auxiliary without changing the meaning.

1.) I think she will get the job.
She could get the job.
She ought to get the job.

2.) I think he should have written to me, but he didn't. (might)
He might have written to me.
He might have written to me!

3.) I can't remember whether he wrote to me or not.
He could have written to me.
He might have written to me.

4.) I think it unlikely that he has been to England - his English is so bad.
He couldn't have been to England.
He can't have been to England.

Thanks in advance for your help.

Best regards,
Dany

[peteryoung]

I have difficulties with model auxiliary too.
What troubles me is the possible/probable thing

The book says may/might/could can all be used to express possibility.
But does "he may have been involved in that crime" implies possibility? Or is it a guess, which should be regarded as probability?

Can we say that 'possible' don't have anything to do with 'guess' ?
Is it true that the sentence "There may be an easier way of solving the problem" means "There definitely is an easier way"?
Or does it mean that There is a probability, say, 30% or 70%, that a easier way exists. Or..? I'm totally confused

[Tdol]

1.) I think she will get the job.
She could get the job.
She ought to get the job.
I'd use 'may well get' to give it a strong possibility. I definitely wouldn't use 'ought to' which suggests that I feel she's right for the job, rather than talking probability.

2.) I think he should have written to me, but he didn't. (might)
He might have written to me.
He might have written to me!
The second is better because the punctuation ahows that it's a criticism.
3.) I can't remember whether he wrote to me or not.
He could have written to me.
He might have written to me.
It think both work here, but would probably use 'might'
4.) I think it unlikely that he has been to England - his English is so bad.
He couldn't have been to England.
He can't have been to England.
The second. The first would refer to a specific time.

[Dany]

Thanks a lot Tdol

[Steven D]

4.) I think it unlikely that he has been to England - his English is so bad.
He couldn't have been to England.
He can't have been to England.

The second. The first would refer to a specific time.

I think "can't have + past participle" is very unlikely to be used in American English. In American, I would expect "could have" to be used in order to express either meaning. If not "could have", then the present perfect would be used. "I don't think he's ever been to England."

He couldn't have lived in England. His English isn't that good. - I don't think it happened.

He couldn't have lived in England even if he wanted to. The government wouldn't allow him to leave. - It was impossible. I think it was impossible.

[Dany]

I think "can't have + past participle" is very unlikely to be used in American English.

Could be, but that was the answer of my book . It is may be in England more used. I don't know it. I only know that the modal auxiliaries makes me infuriatingly

Can somebody please answer my question about "can" and "could"

[Steven D]

Could be, but that was the answer of my book . It is may be in England more used. I don't know it. I only know that the modal auxiliaries makes me infuriatingly

Can somebody please answer my question about "can" and "could"

I think you should go with what tdol said. I was just pointing out what I consider to be another contrast in BE and AE usage.