IIT 2009 level question

The diophantine \frac{1}{x} + \frac{1}{y} = \frac{1}{75} has solutions (75+n₁, 75+n₂) such where n₁n₂ = 75²

So the problem is basically to find number of distinct ways of factoring 75² = 5⁴X3² into two factors

this is like finding two integral resistances whose parallele comb. gives Eq. Res. = 72

so x,y>72 is for sure...........

Explanation for n1n2 = 72²

(x + y) 1
-------------- = ------ .....................(1)
xy 72

Let (x,y) be (72 + n1 , 72 + n2)

Subst. in (1) ,

2*72 + (n1 + n2) 1
------------------------------------ = ------
72² + 72(n1 + n2) + n1n2 72

2*72² + 72(n1 + n2) = 72² + 72(n1 + n2) + n1n2

Hence, n1n2 = 72²

72² = 2⁶ x 3⁴ x 1

Now the question becomes :

" Find the no. of ways in which six 2's , four 3's and one 1 can be divided into two groups such that both groups have at least one element. "

is it necessary for both x and y to be greater than 72 ?

koi toh explain karo naa...muje samaj nahi aa raha hain...woh last step

jeepers...[12] no pbs bhaiyaa ...by da by the last step is not clear to me can u explain it?