I am a biologist and not a real mathematician. Hence some of the answers featured here are sometimes too complicated.
My question is:
I have set of 8 genes named PBX1,ESX1,PIM1,HBB,HBG,BCL11A,KLF4,GATA2
First I wanted to know how many different combinations of 6 I could make without caring about the order. I know now that this can be explained by:
(8x7x6x5x4x3)/(6x5x4x3x2x1) = 28 different combinations
However, the second problem is a bit different. I want to know within these sets of 6 genes how frequently subsets of 4 or 3 or 2 genes are represented (again without caring about the order).
for example: how often does the combination (PBX1,ESX1,PIM1,HBB) occur within these larger sets of 6.
I hope someone is able to help. Please consider my lack of real mathematical knowledge in your answering.
Thanks in advance!!