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The number of possible subsets of {1,2,3.,10} containing '1' as one of its elements?
Most Upvoted Answer
The number of possible subsets of {1,2,3.,10} containing '1' as one of...
Explanation:
To solve this problem, we need to consider two cases:
1. When '1' is included in the subset
2. When '1' is not included in the subset
Case 1: When '1' is included in the subset
In this case, we need to select the remaining 9 elements from {2,3,4,5,6,7,8,9,10}. This can be done in 2^9 ways, as we have two choices for each of the 9 elements - either include it in the subset or exclude it.
Therefore, the number of subsets containing '1' is 2^9.
Case 2: When '1' is not included in the subset
In this case, we need to select all 10 elements from {2,3,4,5,6,7,8,9,10}. This can be done in only one way.
Therefore, the number of subsets not containing '1' is 1.
Total number of subsets containing '1':
The total number of subsets containing '1' is the sum of the number of subsets in Case 1 and Case 2.
Therefore, the total number of subsets containing '1' is 2^9 + 1 = 513.
Conclusion:
The number of possible subsets of {1,2,3.,10} containing '1' as one of its elements is 513.
To solve this problem, we need to consider two cases:
1. When '1' is included in the subset
2. When '1' is not included in the subset
Case 1: When '1' is included in the subset
In this case, we need to select the remaining 9 elements from {2,3,4,5,6,7,8,9,10}. This can be done in 2^9 ways, as we have two choices for each of the 9 elements - either include it in the subset or exclude it.
Therefore, the number of subsets containing '1' is 2^9.
Case 2: When '1' is not included in the subset
In this case, we need to select all 10 elements from {2,3,4,5,6,7,8,9,10}. This can be done in only one way.
Therefore, the number of subsets not containing '1' is 1.
Total number of subsets containing '1':
The total number of subsets containing '1' is the sum of the number of subsets in Case 1 and Case 2.
Therefore, the total number of subsets containing '1' is 2^9 + 1 = 513.
Conclusion:
The number of possible subsets of {1,2,3.,10} containing '1' as one of its elements is 513.
Community Answer
The number of possible subsets of {1,2,3.,10} containing '1' as one of...
10 is the answer according to me...
Let me know is these a right one?
Let me know is these a right one?
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The number of possible subsets of {1,2,3.,10} containing '1' as one of its elements?
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The number of possible subsets of {1,2,3.,10} containing '1' as one of its elements? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The number of possible subsets of {1,2,3.,10} containing '1' as one of its elements? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of possible subsets of {1,2,3.,10} containing '1' as one of its elements?.
The number of possible subsets of {1,2,3.,10} containing '1' as one of its elements? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The number of possible subsets of {1,2,3.,10} containing '1' as one of its elements? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of possible subsets of {1,2,3.,10} containing '1' as one of its elements?.
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