In a survey of brand preference for toothpastes, $82$ of the population (number of people covered for the survey is $100$) liked at least one of the brands: I, II and III. $40$ of those liked brand I, $25$ liked brand II and $35$ liked brand III. If $8$ of those asked, showed liking for all the three brands, then what percentage of those liked more than one of the three brands?

Let n(I)=40, n(II)=25, n(III)=35, and n(I intersection II intersection III)=8. Total union = 82. Using the inclusion-exclusion principle: n(I U II U III) = n(I)+n(II)+n(III) - [n(I int II) + n(II int III) + n(III int I)] + n(I int II int III). 82 = 40+25+35 - S + 8, where S is the sum of double intersections. 82 = 108 - S, so S = 26. The number of people liking exactly two brands is S - 3*n(I int II int III) = 26 - 3*8 = 2. Total liking more than one is 2 + 8 = 10.