Hypergeometric probability explained in multiple ways that are all equivalent

1. Definition:
Mitch is doing a large scale of lncRNA genes that are involved in cancer. We know there are altogether M lncRNA genes, N of which are on his screen list and God who knows everything knows that K out of M lncRNA genes are what God designed for cancer. Assuming Mitch's screen is correctly done. Now the number (x) of genes related to cancer screened by Mitch should follow a hypergeometric distribution.

2. On Mitch's side (Mitch doesn't know God's design)
The probability of getting x hits from the list of N genes from a pool of M genes has to meet these conditions
    x genes chosen from K cancer genes
    N-x genes chosen from M-K non-cancer genes
    altogether N genes chosen from M genes
so the probability should be C(k,x)*C(M-K,N-x)/C(M,N)

3. On God's side (God didn't know Mitch's screening list when he chose the cancer genes to be cancer-causing)
The probability of getting x hits from the list of K cancer genes from a pool of M genes has to meet these conditions
   x Mitch cancer genes chosen from K cancer genes
   K-x Non-Mitch cancer genes were among the M-N non-Mitch-screen genes
   altogether K cancer genes chosen from M genes
so the probability should be C(N,x)*C(M-N,K-x)/C(M,K)

4. These two probability formula are equivalent (equal). In other words, God and Mitch, both not aware of each other's act, have a mathematicallly symmetric position.
   (To prove this you can just expand the combinations into factorials)