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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?
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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
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There are 3 Indians and 3 Chinese in a group of 6 people. How many sub...
To solve this problem, we need to find the number of subgroups that can be formed with at least one Indian in a group of 6 people, which consists of 3 Indians and 3 Chinese.
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, which is 64. This includes all possible combinations with or without Indians.
Step 2: Subgroups without any Indians
We need to subtract the number of subgroups that do not have any Indians from the total number of subgroups. To calculate this, we consider only the Chinese individuals in the group. Since there are 3 Chinese people, the number of subgroups without any Indians is given by 2^3, which is 8.
Step 3: Subgroups with at least one Indian
Now, we can calculate the number of subgroups with at least one Indian by subtracting the number of subgroups without any Indians from the total number of subgroups.
Number of subgroups with at least one Indian = Total number of subgroups - Number of subgroups without any Indians
= 64 - 8
= 56
Therefore, the correct answer is option 'A', 56.
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, which is 64. This includes all possible combinations with or without Indians.
Step 2: Subgroups without any Indians
We need to subtract the number of subgroups that do not have any Indians from the total number of subgroups. To calculate this, we consider only the Chinese individuals in the group. Since there are 3 Chinese people, the number of subgroups without any Indians is given by 2^3, which is 8.
Step 3: Subgroups with at least one Indian
Now, we can calculate the number of subgroups with at least one Indian by subtracting the number of subgroups without any Indians from the total number of subgroups.
Number of subgroups with at least one Indian = Total number of subgroups - Number of subgroups without any Indians
= 64 - 8
= 56
Therefore, the correct answer is option 'A', 56.
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