Melody

Yes absolutely, although there is a high probability that probablility questions isare more perilous than most other types of questions.   LOL

1/cosx(tanx-1)=tanx + cotx/tanx-cotx

You have not used enough brackets, so your question is not clear.

This is what you have asked.  Is it what you really want?

\(\frac{1}{cosx(tanx-1)}=tanx + \frac{cotx}{tanx}-cotx\)

Using the digit 2,3,4,5,6 without repition. How many

a) numbers greater than 40000 can be formed?

the first digit can be 4, 5, or 6 and the others can be any.  So that is

3*4*3*2*1  = 72 ways

b) even numbers greater than 40000 can be formed?

The last can be 2 or 4 or 6 and the first can be 4 or 5 or 6

If the last on is 4 or 6 then there is    2*2*3*2*1 = 24

If the last digit is 2 then there is         1*3*3*2*1  = 18

You have to add those two result together to get the total number.   42 ways

c) odd numbers greater than 40000 can be formed?

The last can be 3 or 5 and the first can be 4 or 5 or 6

If the last on is 3 then there is            1*3*3*2*1  =  18

If the last digit is 5 then there is         1*2*3*2*1  =   12

You have to add those two result together to get the total number.     30 ways

Accept my answer, or anyone elses, at your own peril.     

Of course, thanks Bob, my logic was fine I just didn't read the question properly.  

I didn't realise that the 2 groups of five were studying different subjects. 

Thank you very much :))

Even after you answered it took me ages to realise that I had just not read the question properly.   

Could you please say if my answer would have been right if the there had been no different subjects involved, so that order would not matter. ??  I think it seems right but I am not at all sure ://        

1) No domain restrictions on the first one. It is a standard 4th degree polynomial.

What do you mean? 

333 333 333  is a nine digit number made or 3s

or

3^3*3*3*3*3*3*3*3**3*3*3*3*3^3= 387 420 489 

is a 9 digit number made from 3s 

Which do you have in mind?

What do you want done with this.

In base 10 it is    6.60076229337E+33

I take the first 10 digits to be the first 10 from the right.  Given this definition then the answer will be 0000000000

0.6744302788099833

There are 16 digits afer the point so this will be 

6744302788099833 / 10000000000000000

that is a 1 with 16 zeros after it on the bottom of the fraction.

Mmm good question...

Squared numbers must end in  1,4,9,6,5 or 0

So if your whole number ends in 2,3,7 or 8 then the square root will have to be irrational.

I have not answered your question. I have only looked at the most obvious exclusions.  

Perhaps if you give some specific examples I could tell you what other logic I would use. ://

Maybe someone else would like weigh in?