Pakistan has a huge private sector in eduction and it's rapidly growing.
Pakistan has been increasing enrollment of students in schools at a faster rate since 1990 than India. In 1990, there were 66.2% of Pakistanis vs 51.6% of Indians who had no schooling. In 2000, there were 60.2% Pakistanis vs 43% Indians with no schooling. In 2010, Pakistan reduced it to 38% vs India's 32.7%.
The number of private schools grew 10 fold from about 3000 in 1983 to over 30,000 in 2000.
The rate of private school formation far exceeds the rate of population growth. Using numbers for primary school enrollment in 1983 from Jimenez (578,330 students in the four provinces of Pakistan) and our latest numbers we get an overall increase of 937%, far greater than the 57% population increase (in the same four provinces) between 1981 and 1998. Thus the growth in private school enrollment, even after controlling for population growth, is enormous.
http://economics-files.pomona.edu/andrabi/research/pakschool march29.pdf
What difference does it make? The bottom line is that only 15% of Pak exports are raw materials vs India's 21%.