I haven't worked with pivot tables since Excel97 (?) so aside from losing my feel for how to solve this issue, I'm also not sure if I had ever done anything like this before.
Here's the issue...

This is an abbreviated mockup of the data:
(sorry, I can't post attachments)

Group Q1 Q2 Q3 Q4
A 4 2 3 1
B 2 3 2 0
C 0 1 4 4
D 3 4 0 2
E 1 0 1 3

The result that I am seeking is to determine the number of instances for each of the numbers in the columns.

For instance, Group C has:
1 instance of 0's
1 instance of 1's
2 instances of 4's

Visually it should look like this...

Option 1 4's 3's 2's 1's 0's
A 1 1 1 1 0
B 0 1 2 0 1
C 2 0 0 1 1
D 1 1 1 0 1
E 0 1 0 2 1

Or like this...

Option 2 A B C D E
4's 1 0 2 1 0
3's 1 1 0 1 1
2's 1 2 0 1 0
1's 1 0 1 0 2
0's 0 1 1 1 1


I am able to accomplish this using COUNTIF, however the dataset is actually very large and I was hoping that it could be done using a pivot table instead. I played around with many different ways of positioning the headings, but I can't seem to get the result that I am looking for - or determine if it is even possible (although I assume that it is - which is why I am here asking for guidance).

Could I ask for someone to steer me towards the needed solution?
(btw, I am currently using Excel 2010)