GATE Exam > GATE Questions > There are 3 Indians and 3 Chinese in a group ...
Start Learning for Free
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?
- a)56
- b)52
- c)48
- d)44
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
There are 3 Indians and 3 Chinese in a group of 6 people. How many sub...
No. of sub groups such that every sub group has at least one Indian
Alternate method
Sub groups containing only Indians =
Sub groups containing only Indians =
Most Upvoted Answer
There are 3 Indians and 3 Chinese in a group of 6 people. How many sub...
Problem:
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?
Solution:
To solve this problem, we can use the concept of inclusion-exclusion principle.
Inclusion-Exclusion Principle:
The inclusion-exclusion principle is a technique used in combinatorics to count the number of elements in the union of several sets.
Step 1: Total number of subgroups:
The total number of subgroups that can be formed from a group of 6 people is given by 2^6 - 1 = 63, where 2^6 represents the number of possible combinations and 1 is subtracted to exclude the empty subgroup.
Step 2: Subgroups without any Indian:
To find the number of subgroups without any Indian, we need to choose all the people from the Chinese group. Since there are 3 Chinese people, the number of subgroups without any Indian is given by 2^3 - 1 = 7, where 2^3 represents the number of possible combinations of Chinese people and 1 is subtracted to exclude the empty subgroup.
Step 3: Subgroups with at least one Indian:
To find the number of subgroups with at least one Indian, we subtract the number of subgroups without any Indian from the total number of subgroups.
Number of subgroups with at least one Indian = Total number of subgroups - Subgroups without any Indian
= 63 - 7
= 56
Therefore, the correct answer is option A) 56.
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?
Solution:
To solve this problem, we can use the concept of inclusion-exclusion principle.
Inclusion-Exclusion Principle:
The inclusion-exclusion principle is a technique used in combinatorics to count the number of elements in the union of several sets.
Step 1: Total number of subgroups:
The total number of subgroups that can be formed from a group of 6 people is given by 2^6 - 1 = 63, where 2^6 represents the number of possible combinations and 1 is subtracted to exclude the empty subgroup.
Step 2: Subgroups without any Indian:
To find the number of subgroups without any Indian, we need to choose all the people from the Chinese group. Since there are 3 Chinese people, the number of subgroups without any Indian is given by 2^3 - 1 = 7, where 2^3 represents the number of possible combinations of Chinese people and 1 is subtracted to exclude the empty subgroup.
Step 3: Subgroups with at least one Indian:
To find the number of subgroups with at least one Indian, we subtract the number of subgroups without any Indian from the total number of subgroups.
Number of subgroups with at least one Indian = Total number of subgroups - Subgroups without any Indian
= 63 - 7
= 56
Therefore, the correct answer is option A) 56.
|
Explore Courses for GATE exam
|
|
Similar GATE Doubts
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?a)56b)52c)48d)44Correct answer is option 'A'. Can you explain this answer?
Question Description
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?a)56b)52c)48d)44Correct answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about 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?a)56b)52c)48d)44Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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?a)56b)52c)48d)44Correct answer is option 'A'. Can you explain this answer?.
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?a)56b)52c)48d)44Correct answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about 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?a)56b)52c)48d)44Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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?a)56b)52c)48d)44Correct answer is option 'A'. Can you explain this answer?.
Solutions for 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?a)56b)52c)48d)44Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of 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?a)56b)52c)48d)44Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
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?a)56b)52c)48d)44Correct answer is option 'A'. Can you explain this answer?, a detailed solution for 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?a)56b)52c)48d)44Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of 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?a)56b)52c)48d)44Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice 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?a)56b)52c)48d)44Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup