At the end of a business conference the 12 people present there shake hands with each otheronce. How many handshakes will there be altogether?(A) 55 (B) 66(C) 56 (D) 132
Question
At the end of a business conference the 12 people present there shake hands with each otheronce. How many handshakes will there be altogether?(A) 55 (B) 66(C) 56 (D) 132
Solution
To find the total number of handshakes, we can use a combination formula.
Step 1: Determine the number of ways to choose 2 people out of 12. This can be calculated using the combination formula: nCr = n! / (r!(n-r)!), where n is the total number of people and r is the number of people chosen at a time. In this case, n = 12 and r = 2.
Step 2: Calculate the combination: 12C2 = 12! / (2!(12-2)!) = 12! / (2!10!) = (12 * 11) / (2 * 1) = 66.
Therefore, there will be a total of 66 handshakes.
The correct answer is (B) 66.
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