Since question says we need at least one Indian. We need to consider below cases:
Case 1:
1 Indian (0 Chinese + 1 Chinese + 2 Chinese + 3 Chinese) ==> 3C1 * (3C0 + 3C1 + 3C2 + 3C3)
Case 2:
2 Indians (0 Chinese + 1 Chinese + 2 Chinese + 3 Chinese) ==> 3C2 * (3C0 + 3C1 + 3C2 + 3C3)
Case 3:
3 Indians (0 Chinese + 1 Chinese + 2 Chinese + 3 Chinese) ==> 3C3 * (3C0 + 3C1 + 3C2 + 3C3)
To find the no. of subgroups, we need to consider all the 3 cases.
no. of sub groups = 3C1 * (3C0 + 3C1 + 3C2 + 3C3) + 3C2 * (3C0 + 3C1 + 3C2 + 3C3) + 3C3 * (3C0 + 3C1 + 3C2 + 3C3)
= (3C0 + 3C1 + 3C2 + 3C3) * (3C1 + 3C2 + 3C3)
= 8 * 7
= 56