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In a birthday party,7 friends meet.each friends shook hands with each other exactly once.how many shake hands are there?
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In a birthday party,7 friends meet.each friends shook hands with each ...
Understanding Handshakes Among Friends
In a gathering of friends, each person shakes hands with every other person exactly once. To calculate the total number of handshakes, we can use a combinatorial approach.
Formula for Handshakes
The number of unique handshakes can be determined using the formula for combinations, specifically choosing 2 friends out of n:
- Total Handshakes = n(n - 1) / 2
Here, n represents the number of friends.
Calculation for 7 Friends
For 7 friends:
- n = 7
Now, substituting into the formula:
- Total Handshakes = 7(7 - 1) / 2
- Total Handshakes = 7 * 6 / 2
- Total Handshakes = 42 / 2
- Total Handshakes = 21
Conclusion
Thus, in a birthday party where 7 friends meet and each shakes hands with every other friend exactly once, there are a total of:
- 21 handshakes.
This formula and method can be applied to any group size to find the total number of unique handshakes, making it a valuable tool in combinatorial counting.
In a gathering of friends, each person shakes hands with every other person exactly once. To calculate the total number of handshakes, we can use a combinatorial approach.
Formula for Handshakes
The number of unique handshakes can be determined using the formula for combinations, specifically choosing 2 friends out of n:
- Total Handshakes = n(n - 1) / 2
Here, n represents the number of friends.
Calculation for 7 Friends
For 7 friends:
- n = 7
Now, substituting into the formula:
- Total Handshakes = 7(7 - 1) / 2
- Total Handshakes = 7 * 6 / 2
- Total Handshakes = 42 / 2
- Total Handshakes = 21
Conclusion
Thus, in a birthday party where 7 friends meet and each shakes hands with every other friend exactly once, there are a total of:
- 21 handshakes.
This formula and method can be applied to any group size to find the total number of unique handshakes, making it a valuable tool in combinatorial counting.
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In a birthday party,7 friends meet.each friends shook hands with each other exactly once.how many shake hands are there?
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In a birthday party,7 friends meet.each friends shook hands with each other exactly once.how many shake hands are there? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In a birthday party,7 friends meet.each friends shook hands with each other exactly once.how many shake hands are there? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a birthday party,7 friends meet.each friends shook hands with each other exactly once.how many shake hands are there?.
In a birthday party,7 friends meet.each friends shook hands with each other exactly once.how many shake hands are there? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In a birthday party,7 friends meet.each friends shook hands with each other exactly once.how many shake hands are there? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a birthday party,7 friends meet.each friends shook hands with each other exactly once.how many shake hands are there?.
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