Directions: These questions are based on the following information: Children in a class play only one or two or all of the three games - badminton, football and cricket. 5 children play only cricket, 8 children play only football and 7 children play only badminton. 3 children play only two games - badminton and football, 4 children play only two games - cricket and football, and another 4 children play only two games - badminton and cricket. 2 children play all the three games. In all, how many children play football?

### Concept & Strategy Finding the total number of students who play a specific game requires summing every distinct region inside that game's Venn diagram circle. $$n(F) = n(\text{Only } F) + n(\text{Only } F \text{ and } B) + n(\text{Only } F \text{ and } C) + n(\text{All three})$$ ### Step-by-Step Solution * **Given:** * Only football = $8$ * Only football and badminton = $3$ * Only football and cricket = $4$ * All three games = $2$ * **Calculation:** * We need the total sum of the Football circle. * Add the exclusively football players, the two sets of dual-sport players involving football, and the multi-sport players. * Total Football = $8 + 3 + 4 + 2$ * Total Football = $17$ ### Exam Strategy & Shortcut Scan the paragraph specifically for the word "football" and immediately write down the associated numbers: $8$ (only), $3$ (with badminton), $4$ (with cricket), and the universal center $2$. Sum them up directly without drawing a diagram. ### Common Pitfall A major error is misreading "In all, how many play football" as "How many play ONLY football." Always look for the word "only" to dictate whether you need a single region or the whole circle sum. ### Final Answer **Therefore, the correct answer is 17.**