When ten persons shake hands with one another, in how many ways is it possible?
- A20
- B25
- C40
- 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.
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