In a party 15 people shake their hands with each other. How many times did the hand-shakes take place?
(a)105
(b)120
(c)135
(d)165
Answer
Answer (as printed): A
Explanation
Clearly, first man shakes hand with all other 14 men; second man shakes hand with 13 men (other than first man); third shakes hand with 12 men and so on. $$\begin{aligned} \therefore \text { Total number of hand-shakes } & =(14+13+12+\ldots . .+1) \\ & =\frac{14 \times 15}{2}=105 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.