Discussion
There are 3 Indians and 3 Chinese in a group of 6 people. How many subgroups of this group can we choose so that every subgroup has at least one Indian?
Answer: A
There are 56 such subgroups.
Count all subgroups and remove those with no Indian. A group of 6 people has \(2^{6} = 64\) subsets. Those with no Indian are the subsets of the 3 Chinese only, \(2^{3} = 8\) of them (including the empty set). So
\[ 64 - 8 = 56 \]
Equivalently, choose any non-empty set of Indians (\(2^{3} - 1 = 7\) ways) and any set of Chinese (\(2^{3} = 8\) ways): \(7 \times 8 = 56\). The empty subgroup is automatically excluded, since it has no Indian. 52, 48 and 44 come from subtracting further cases that do in fact contain at least one Indian.
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development