There can be infinite number of handshakes, if they are Chinese and Pakistanis as they will repeatedly shake hands with each other...
If 5 of them are boys and 5 girls and room is under Taliban Regime, there will be 20 handshakes (Girls with girls boys with boys)
If they are french, there will be loads of kisses hardly a handshake...
If they are a group of Indians and Pakistanis, There will be 90 handshakes if Kashmir is not discussed (Just to over-emphasize their friendliness) and Zero if it is discussed (They will pull out swords for fighting)
If they are a group of Pakistanis and Americans 3 Pakistanis will not shake hands as they dot trust americans and 3 Americans will not shake Hands as they think abstaining one's are Jihadis. 2 Americans and 2 Pakistanis will have handshakes every time Americans give money and Pakistanis are keeping in their pocket. (They are Polititions)
If this is a simple maths problem then there will be 45 handshakes.
Any more combinations friends....