Question

There are 3 Indian and 3 Chinese in a group of 6 people. How many subgroups of this group can be chosen so that ever subgroups has atleast one Indian.

Answer 1

Number of sub groups required = Total subgroups possible - Subgroups having                                                                                                   no Indian
                                                   = $2^{6}$ - (1 + 3 + 3 + 1)
(Because subgroups having no indian = subgroups with no chinese + subgroups with 1 chinese + subgroups with 2 chinese + subgroups with 3 chinese)
                                                   = 64 - 8 = 56