Calculating the number of possible paths through some squares I'm prepping for the GRE.
Would appreciate if someone could explain the right way to solve this problem. It seems simple to me but the site where I found this problem says I'm wrong but doesn't explain their answer. So here is the problem verbatim:

Find the number of paths from x to y moving only right (R) or down (D).
My answer is 6. What am I missing??
Thanks for any help.

See here you can easily compute the number of paths by applyinfg the COMBINATION concept.
So what is the concept!!
ok then.....let us consider to proceed from x to y we have to take the steps to the direction of  RIGHT and DOWN....fine?
and let us take RIGHT = R and DOWN = D.....still fine.. :-)
now see if anyone wants to go from X to Y he must take 2 DOWN steps and atmost 6 RIGHT step.
So we can say that we have to take total 8 numbers of step.You can check it by your own that we must take 8 steps to reach at Y starting from X poit.ok.
and see here we can write a combination of  steps,like:   {  R-R-R-R-D-R-D-R  }      -----(see its a suitable traverse path.match this path with the picture.)
And now we can make our main observation on this problem.....So what is it?
See, you have to take total of 8 steps and all of them are the combination of R and D's ok?
And the observation is: You have to take just 2 D(DOWN step) and also just 6 R(RIGHT step) to reach at Y.
So we can say that the total number of combination is:  HOW MANY COMBINATION OF 'R' OR 'D' is possible from the total of 8 steps!!!!!
The required answer is actually the combination of  2 PLACES for D's OR 6 PLACES for R's from 8 total steps(OR TOTAL 8 PLACES where R and D letters take place)........ 
see here we are just mapping our problem of counting the number of 
suitable paths from X to Y into a basic counting problem.....And we just logically made a connection between these two problems and it is clear that if we can calculate the combination of 2 PLACES for  D's OR 6 R's from total 8 steps it will be enough!!
Here is the total of 8 places where D and R may take places:

{ ___  ___  ___  ___  ___  ___  ___  ___ }

And we actually CHOOSE 2 places for for 2 D's OR we CHOOSE 6 places for 6 R's but we dont bother for the oreding of D's OR R's.....the 2 D's OR the 6 R's can tale place randomly but their requirement for the places is fixed!! it is 2 for 2 D's and it is 6 for 6 D's......actually choosing 2 D's OR 6 R's are basically same!! :-)  
So, the answer is :    8C2 or 8C6   (note that both are same!! :-) )
8C2 =  28 and easily you can see 8C6 = 28.
SO, THERE ARE 28 PATHS FROM X TO Y!!
