32 ways
Dancing- d, singing- s, rapping- r
Skill set as per trainee, 7 possible options as:
1- dsr
2- ds
3- dr
4- sr
5- d
6- s
7- r
Options of 3 trainees with required skill test:
1. dsr+ any 2 others --> 15 ways
2. ds+ 2 others with r included in any --> 4+3+1+1= 9 ways
3. dr+ 2 others with s included in any --> 3+2= 5 ways
4. sr+ 2 others with d included in any --> 2 ways
5. d+s+r --> 1 way
Total- 15+9+5+2+1= 32 ways