You never need to appologise for admitting that you do not understand.  we want you to learn.  We do not to pretend to learn.

there are 144 ways those people can sit together. BUT the question asks you how many ways can they be seated so that they are NOT together.  That is why I subtracted from the total number of seating arrangements possible which is 7!

Oh my way any 2 of those guys can sit together, just not all 3 of them. :)

What is the probability that 7 people can seat with a certain 3 people not in a consecutive order?

Lets so those 3 people are glued together.

Then it would be like seating 4 people.  

Sorry I can't count it would be 4 people and the cojoined triplets - that is 5 'bodies'.  I will correct it from here.

there are 5! ways of sitting 5 people in a  row = 120 ways

now thos 3 people can be joined together in any order so ther would be 3! ways = 6 ways.

So ther are 120*6= 720 ways those 3 people can be seated together.

now there are 7! ways of seating 7 people in a row.  That is 5040 ways

5040-720=4320  so there are 4320 ways to seat everyone without those 3 individuals sitting together.

So the prob that they will not be sitting together is  4320/5040

$${\frac{{\mathtt{4\,320}}}{{\mathtt{5\,040}}}} = {\frac{{\mathtt{6}}}{{\mathtt{7}}}} = {\mathtt{0.857\: \!142\: \!857\: \!142\: \!857\: \!1}}$$

Now it is a running joke around here - none of us are really probablity experts. So don't trust me to much :))

CPhill answer and mine now agree.  I believe this answer is correct    

Are they sitting in a row or around a table?

Can 2 of those people sit together?

Not real high.  We must be sick.  This is a real anomoly.  LOL 

I wish you had not asked the same question twice - it causes confusion.

You can do it straight on the forum calc

$${\frac{{\mathtt{299}}}{{\mathtt{5}}}} = {\mathtt{59.8}}$$

or you can say

how many 5s in 29  well  that 5 with four left over

then  how many 5s in 49 that is 9 with four left over

so the answer is 59 remainder 4

or

$$59\frac{4}{5}$$

which can also be written as 59.8      

Yes your way is neat too Chris :)

But inverse cos  (or acos) is where you have the ratio and your answer is an angle.

THIS one id the other way around.

You have the angle and you want the Cos ratio.  

that is why I think that there is an error in your question.  

cos((3*sqrt(3)+4) /(5*sqrt(10))

Are you sure that your question is correct??

$$\\Cos\;\frac{(3\sqrt3+4)}{5\sqrt{10}}\\\\$$

If this angle is in radian then it =0.8355

if it is in degrees then it is.

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\frac{\left({\mathtt{3}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{3}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{4}}\right)}{\left({\mathtt{5}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{10}}}}\right)}}\right)} = {\mathtt{0.999\: \!948\: \!477\: \!928}}$$

$${\frac{{\mathtt{35.22}}}{{\mathtt{1\,056}}}} = {\mathtt{0.033\: \!352\: \!272\: \!727\: \!272\: \!7}}$$

Approx 3.33 cents each