UPSC Prelims 2010·GS1·science-and-technology·science and technology

When ten persons shake hands with one another, in how many ways is it possible?

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Last updated 23 May 2026, 3:31 pm IST
  1. A20
  2. B25
  3. C40
  4. D45Correct

Explanation

To find the number of handshakes among ten people, we use the concept of combinations because a handshake occurs between two individuals and the order does not matter. In a group of n people, the formula for the total number of handshakes is n multiplied by n minus 1, divided by 2. Here, n is 10. Plugging the number into the formula: 10 multiplied by 9 equals 90. 90 divided by 2 equals 45. Alternatively, you can think of it this way: the first person shakes hands with 9 others, the second person with 8 others (already counted the first), the third with 7, and so on. Adding 9 plus 8 plus 7 plus 6 plus 5 plus 4 plus 3 plus 2 plus 1 equals 45. Therefore, the correct option is D.
science-and-technology: When ten persons shake hands with one another, in how many ways is it possible?

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