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method 1 ⇒The formula is 
number of handshakes = n (n-1)/2
                                      = (15×14)/2
Method 2,
15th man handshake with 14 man
14th man handshake with 13 man, since he already hand shaken with 15th man and so on.
So, the total number of ways = 14 + 13+12+11+....1 = 105 ways

hope you understand both methods .... :)
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N(n-1)/2 =15(14)/2=15(7)=105