We can use inclusion-exclusion principle (IEP). Well, IEP was not part of this test, but still.
#(At least one Indian and at least one American) = #(Total ways) – #(no Indian or no American)
= 2^7. (We have 2 choices for each person –> either choose or reject)
#(No Indian or no American) = #(no Indian) + #(no American) – #(no Indian and no American)
= 2^4 (choose/reject from Americans only) + 2^3 (choose/reject from Indians only) – 1 (choose no one)
= 16 + 8 -1 = 23
Hence, #(at least one Indian and at least one American) =
128 – 23 = 105.