Very hard math question – need help fast

Question

"There are 57 students. 18 Greek, 13 Finns, 6 Russians and 20 Swedes. The students study in groups. A group always consists of one or more students. If a group has at least 2 students that are of same nationality, then the group has to have at least one student who is different nationality. How many different ways are there to divide the 57 students to groups?"

Answer 1

Based on the question and follow up comments, the probability combination formula can be used to find an estimate. Order doesn't matter and repetition, same Peron in more than one group, not specified.

 

C (n, r) where n = number of people chosen for groups = 57

                         r = minimum group size = 2

 

n!/r!(n-r)! = 57!/2!(57-2)! = 57 x 56 x 55 x 54 x 53...../2(55!)

 

= 57 x 56 x 54 v 53..../2(55 x 54 x 53...) 

 

= 57 x 56 x 55/2

 

= 175, 560/2 

 

= 87, 780 possible ways to choose 2 people from 57