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I don't know about primary education (ages 6-10), but for secondary and tertiary education, here is the breakdown for Bangladesh:
General Education - 8,851,102 students (83.07%)
Madrasah Education - 1,587,373 students (14.90%)
Technical Vocational Education - 122,309 students (1.15%)
Professional Education - 94,624 students (0.89%)
Madrasahs in Bangladesh are run or supervised by the state, and a Madrasah Education Board supervises curriculum and administers the country's education testing (which basically mirrors the British system, O and A levels and the like).
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