## Realated Questions

In a survey of political preference, 78% of those asked were in favour of at least one of the proposals: I, II and III. 50% of those asked favoured proposal I, 30% favoured proposal II, and 20% favoured proposal III. If 5% of those asked favoured all three of the proposals, what percentage of those asked favoured more than one?

Consider the set S = { 1, 2, 3, ... , 1000}. How many arithmetic progressions can be formed from the elements of S that start with 1 and end with 1000 and have at least 3 elements?

In a tournament, there are n teams T

_{1}, T_{2}....,T_{n}, with n > 5. Each team consists of k players, k > 3. The following pairs of teams have one player in common. T_{1}& T_{2}, T_{2}& T_{3}, ...,T_{n-1}& T_{n}and T_{n}& T_{1}

No other pair of teams has any player in common. How many players are participating in the tournament considering all the n teams together?