In a language club, 5 members speak only Hindi, 4 speak only Tamil and 3 speak both languages. A sub-group of 3 members is to be formed in which every member can speak Hindi. In how many ways can it be formed?

'Can speak Hindi' covers the 5 Hindi-only members TOGETHER WITH the 3 who speak both — 8 people in all — and any 3 of those 8 will do: C(8,3) = 56. Trap 10 = C(5,3) counts only the Hindi-only members and forgets that the bilingual members speak Hindi too; overlapping groups are the whole point of the question. Trap 220 = C(12,3) picks any 3 of the 12 members and ignores the condition. Trap 35 = C(7,3) does the same job for the 4 + 3 = 7 Tamil speakers and answers the wrong language.