Find number of possible groups of 6 sets of 4 different variables without duplicate variables within a set.

Question

Starting with 24 variables A,B,C,...X. Trying to come up with as many sets of 4 variables, using all 24, as in 6 groups of 4 variables, without having any 2 variables in the same set twice.

So, if group one is sets: abcd efgh ijkl mnop qrst uvwx, then subsequent groups cannot have point A with B, C, or D; E with F, G, or H; etc..

Answer 1

If I understand your question correctly you have 24 different items (named A, B, ...x)

From those 24 items you want to form sets of size 4.

You want to know how many different such sets there are....I think!

The answer to that question is ₂₄C₄=24*23*22*21/4!=23*22*21.