Handshakes across two groups

At a networking mixer there are 6 analysts and 4 traders. Every analyst shakes hands with every other analyst and with every trader, but the traders - who all know each other - do not shake hands among themselves. How many handshakes occur in total?

Show hints (2)+
  1. Split into analyst–analyst, analyst–trader, and trader–trader pairs.
  2. Or take all (102)\binom{10}{2} pairs and subtract the (42)\binom{4}{2} trader pairs.

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39

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Asked at: Timed Mental-Math & Sequences, Game-Based Aptitude

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