Question

5 Nephrologists decide to hold daily meetings such that (i) At least one Nephrologist attend each day. (ii) A different set of Nephrologists must attend on different days. (iii) On day N for each 1 ≤ d < N, at least one Nephrologist must attend who was present on day d. How many maximum days can meetings be held?

• A. 14
• B. 16
• C. 20
• D. None of these

Answer 1

The correct option is B 16

We need to find the largest possible number of subsets of {1, 2, 3, 4, 5} such that no 2 subsets are disjoint. Fix one element from the set to be presented in each subset and we can have $2^4$ such possibilities.

Because one element is common. So, remaining 4 can be selected ${}^4{C}_0{+}^4{C}_1{+}^4{C}_2{+}^4{C}_3{+}^4{C}_4=2^4=16$ ways. There are total 16 days.