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Fifteen people from different places come together for a family reunion. Each one of them had two gifts each for every other person. When the gifts were exchanged they hugged each other. What is the difference between the number of hugs and the number of gifts exchanged?
Each one of them had two gifts each for every other person. Thus, each one of them is carrying $$2\times14=28$$ gifts with them. Thus, the total number of gifts in the function is $$=28\times15=420$$ gifts.
Total number of hugs $$=^{15}C_2=105$$ hugs
Difference between the total number of hugs and the total number of gifts $$=420-105=315$$
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