When ten persons shake hands with one another, in how many ways is it possible? (UPSC Prelims 2010)

Question

The number of ways ten persons can shake hands with one another is the number of unique handshakes, given by the combination formula C(n, 2) = n(n - 1)/2, where n = 10. This calculates as (10 × 9)/2 = 45. Since handshakes are undirected and no one can shake hands with themselves, each pair shakes hands only once. This is a common combinatorial problem representing edges in a complete graph K₁₀, resulting in 45 unique handshakes.

GKToday Admin · Accepted Answer

45 The number of ways ten persons can shake hands with one another is the number of unique handshakes, given by the combination formula C(n, 2) = n(n - 1)/2, where n = 10. This calculates as (10 × 9)/2 = 45. Since handshakes are undirected and no one can shake hands with themselves, each pair shakes hands only once. This is a common combinatorial problem representing edges in a complete graph K₁₀, resulting in 45 unique handshakes.

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