Math
posted by Amy on .
While spending 10 weeks at a university in Germany, Ayesha frequently had dinner with 5 of her classmates: Jack, Erik, Annalee, Peter, and Nola. She ate dinner with each of these classmates exactly 12 times. She ate dinner with every pair of them eight times. She ate dinner with every set of 3 classmates ten times. She ate dinner with every foursome five times. She ate with all five classmates four times. On how many days did Ayesha have dinner with none of these classmates?

10 Weeks = 70 days
12 + 8 + 10 + 5 + 4 = ?
Subtract the above answer from 70.