Melody

I think Geno may have answered for if everything is distinguishable.

If the b***s and the boxes are not distinguishable   (the same)  then

the only difference is how many are in the boxes.

5,0,0

4,1,0

3,2,0

3,1,1

2,2,1

I think that is it.

5 possibilities     

Yep - looks good to me :)

write an equation passing through the point and parallel to the given line (-2, 3);      y= -1x + 4

Well the gradient will be 1.

so ther are lots of ways to do it now.

I like  to say

gradient = gradient

$$1=\frac{y-3}{x--2}$$

etc

Thanks Geno,

I would not have thought of that. :)

Geno gave you an excellent answer anon.  I am appalled by your rudeness!

cosec 61 = 1/sin61

WHY is this the answer Nauseated?  Can you please explain?

Hi Anon :)

We do not have time to answer every question and if a question falls back to the second or 3rd page it has likely already been answered from somewhere else.  For this reason, old questions are not given priority.

We encourage people to repost just as you have done here except it would be better if you draw specific attention to your own question.

If you did that, I would give your question very high priority.  I think CPhill would too  :)

I am not over confident either but I will give it a go

There are 16 points in this region so there are  16C3 = 560   ways of choosing 3 of these points.

Now you have to take away all the sets of collinear points (those that form a line)

There a 4 points in every row and every column.  And there are 4 rows and 4 columns

the number of ways that 3 collinear points can be chose from these is 8* 4C3 = 8*4 = 32

Now there are also 4 points in each of the central diagonals so this is   2*4C3 = 2*4=8

now the diagonal next to the cetral diagonal has 3 points and there are 4 of these   = 1*4=4

so I think that the answer is

$${\mathtt{560}}{\mathtt{\,-\,}}{\mathtt{32}}{\mathtt{\,-\,}}{\mathtt{8}}{\mathtt{\,-\,}}{\mathtt{4}} = {\mathtt{516}}$$     ways that a triangle can be formed.  :)

Thanks Nauseated:)

Sorry Bertie, somehow I overlooked giving you points - I have rectified this oversite now.  :)

I really appreciate you helping me improve my probability abilities :)