We can concentrate on one set of 5 letters as the same would replicate in other sets.
Let us take the first five numbers. There are no As

1) All are same
All can be Bs, then next five will be Cs and next five As
Or all can be Cs, then all As and then all Bs
2 ways

2) 4 Bs and 1 C
Then the next five will contain 4 Cs and 1 As, and last five will be 4 As and 1 Bs
Total 5C4 for each = 5C4*5C4*5C4=5*5*5=125

3) 3Bs and 2 Cs
Similar as above => 5C3*5C3*5C3=10*10*10=1000

4) 3Cs and 2Bs
5C2*5C2*5C2=10*10*10=1000

5) 4Cs and 1 Bs
Total 125

Total 2+125+1000+1000+125=2252

E