Dinner Party!

Discrete Mathematics Level pending

I have six friends and during a certain vacation, I met them during several dinners. I found that I dined with all the six exactly on one day; with every five of them on 2 days;with every four of them on 3 days;with every three of them on 4 days;with every two of them on 5 days. Further every friend was present at 7 dinners and every friend was at 7 dinners. How many dinners I have alone?

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