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12 friends met at a party. Each friend shook hands with each other exactly once. Number of handshakes took place is _____.
- a)66
- b)50
- c)45
- d)40
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
12 friends met at a party. Each friend shook hands with each other exa...
The first person shook hands with 11 remaining people, the second person also shook hands with 11 people, but we count 10, as the hand shake with the first person has already been counted.
Then add 9 for the third person, 8 for the fourth one & proceeding in this fashion
We get: 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 66.
Most Upvoted Answer
12 friends met at a party. Each friend shook hands with each other exa...
**Solution:**
To find the number of handshakes that took place, we need to find the number of ways to choose two friends out of the 12 friends.
We can solve this problem using combinations.
**Combinations:**
In a combination, the order of the elements does not matter.
The formula to find the number of combinations is:
nCr = n! / (r! * (n-r)!)
Where n is the total number of objects, and r is the number of objects to be chosen.
**Number of Handshakes:**
In this problem, we need to find the number of ways to choose 2 friends out of 12 friends, which represents the number of handshakes that took place.
Using the combination formula, we can calculate the number of handshakes:
12C2 = 12! / (2! * (12-2)!)
= 12! / (2! * 10!)
= (12 * 11 * 10!) / (2! * 10!)
= (12 * 11) / 2!
= 132 / 2
= 66
Therefore, the number of handshakes that took place is 66.
Hence, the correct answer is option A) 66.
To find the number of handshakes that took place, we need to find the number of ways to choose two friends out of the 12 friends.
We can solve this problem using combinations.
**Combinations:**
In a combination, the order of the elements does not matter.
The formula to find the number of combinations is:
nCr = n! / (r! * (n-r)!)
Where n is the total number of objects, and r is the number of objects to be chosen.
**Number of Handshakes:**
In this problem, we need to find the number of ways to choose 2 friends out of 12 friends, which represents the number of handshakes that took place.
Using the combination formula, we can calculate the number of handshakes:
12C2 = 12! / (2! * (12-2)!)
= 12! / (2! * 10!)
= (12 * 11 * 10!) / (2! * 10!)
= (12 * 11) / 2!
= 132 / 2
= 66
Therefore, the number of handshakes that took place is 66.
Hence, the correct answer is option A) 66.
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12 friends met at a party. Each friend shook hands with each other exa...
66
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12 friends met at a party. Each friend shook hands with each other exactly once. Number of handshakes took place is _____.a)66b)50c)45d)40Correct answer is option 'A'. Can you explain this answer?
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