Dividing 4 people into 4 groups

[mobius0]

A group of 100 people are divided evenly into 4 subgroups. There are 4 friends within the groups. What is the probability that the 4 friends will be in 4 different groups?

I believe I have solved this but I am not sure if it is correct. Here is what I have done:

E1 = Probability of person A in any group = 1
E2 = Probability of person A and B in different groups = 75/99
E3 = Probability of person A, B, and C in different groups = 50/98
E4 = Probability all 4 people are in different groups = 25/97

P(E1E2E3E4) = (75*50*25)/(99*98*97) = .0996
How does this look?

Thanks

[CowboyBear]

Looks right to me