In a group of 30 individuals, if everyone shakes hands with everyone else, how many total handshakes occur?
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Answer: B. 435
Explanation
Every individual in a group shakes hands with every other person exactly once without duplicate counting. The mathematical formula for calculating total pairwise handshakes in any group is n multiplied by n minus one over two. Substituting thirty individuals into the handshake formula yields thirty multiplied by twenty-nine divided by two. Combinatorics combinations formulas determine the number of ways to choose pairs from a larger group of items. Handshake problems represent classic undirected graph edge counting exercises in discrete mathematics. Multiplying thirty by twenty-nine gives eight hundred seventy, which when halved yields four hundred thirty-five.
Event planners calculate networking interaction counts for conference receptions using pairwise combination formulas. Network engineers determine total direct communication connection links required between computers in a mesh topology. Sociologists study social network interaction densities by counting pairwise relationship connections in groups. Option A suggests eight hundred seventy which forgets to divide the product by two to eliminate duplicates. Option C suggests thirty factorial which vastly overcounts possible handshakes using permutation factors. Option D suggests twenty-nine factorial plus one which is an incorrect mathematical formula for combinations.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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