Differences between the two formulas for advanced overlapping sets

1. The two formulas are used depending upon the information given in the question.
If info on sum of 2 groups is given then use the first formula and
if info on sum of exactly 2 group is given then use the second formula

(Refer Diagram attached)
2. We have three types of overlap=> two set overlap - 3 (region 1, 2 and 3)
exactly 2 group overlap - 3 (region x,y and z)
three set overlap - 1 (all three)

3. Formula 1 - info on sum of 2 group is given
Tot = A + B + C - (sum of 2 group overlaps) + (all 3) + neither
Note:
In the Sum of A + B + C, the sum of two group overlap region i.e sum of 1, 2 and 3 is counted twice
and All three region is counted thrice (once with each set A, B and C)
so, we subtract sum of two group overlap region (1+2+3) once
but when we perform A+B+C - sum of 2 group overlaps then all three region is not counted even once (note that all three region is counted thrice in sum of A+B+C and thrice in sum of 2 group overlap, hence get subtracted), so we need to add all three region once in the formula above.

4. Formula 2 - info on sum of exactly 2 group is given
Tot = A + B + C - (sum of EXACTLY 2 group overlaps) - 2 * (all 3) + neither
Here, in the Sum of A + B + C, the sum of exactly 2 group overlap region i.e x, y and z is counted twice
and All three region is counted thrice
so, we subtract sum of two group overlaps (x+y+z) once and all three region twice