At the end of a business conference, 10 people present shake hands with each…
2014
At the end of a business conference, 10 people present shake hands with each other once. How many handshakes will be there all together?
Answer: B. 45 — The handshake problem is a classic combinatorics problem. A handshake requires two people. The number of handshakes is equivalent to the number of ways to…
- A.
20
- B.
45
- C.
55
- D.
90
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Correct answer: B
The handshake problem is a classic combinatorics problem. A handshake requires two people. The number of handshakes is equivalent to the number of ways to choose 2 people from a group of 10, without regard to the order of selection.
This can be solved using the combination formula, which is C(n, k) = n! / (k!(n-k)!).
For this problem, n = 10 (the number of people) and k = 2 (the number of people in a handshake).
The calculation is C(10, 2) = 10! / (2!(10-2)!) = 10! / (2! * 8!).
This simplifies to (10 * 9) / 2 = 90 / 2 = 45.