employees have the choice of one of 3 schemes a,b or c. they must vote for one but if they have no preference, they can vote for all 3 or if against one scheme, they can vote for the one they prefer. a sample poll of 200 votes revealed (i) 15 would vote for a and c but not b (ii) 65 would vote for b only, 51 would vote for c only, 15 would vote for a and b, 17 would vote for either a or b or both a and b but not c, 128 would vote for either b or c or both b and c but not a. How many would vote for all these schemes, only one scheme, a only, all irrespective of b or c, a and b but not c

Question

employees have the choice of one of 3 schemes a,b or c. they must vote for one but if they have no preference, they can vote for all 3 or if against one scheme, they can vote for the one they prefer. a sample poll of 200 votes revealed (i) 15 would vote for a and c but not b (ii) 65 would vote for b only, 51 would vote for c only, 15 would vote for a and b, 17 would vote for either a or b or both a and b but not c, 128 would vote for either b or c or both b and c but not a. How many would vote for all these schemes, only one scheme, a only, all irrespective of b or c, a and b but not c

Answer 1

when you say

17 would vote for either a or b or both a and b but not c

that seems unlikely that (aUb)U(a∩b∩c') is only 17, since we already know that a∩b = 15

I think the wording is very confusing.