Ghazni governor's office said 12 of the wounded are female students of Ghazni University which is located on the outskirts of the provincial capital.
A bomb had been left in a motorcycle that detonated as a minibus of recruits for Afghan security forces passed, Nangarhar officials say. There has been no immediate claim of responsibility so far.
Afghanistan's Independence Day celebrations have been ripped apart by a series of attacks as Afghans face a concerted push from Daesh in the country.
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Among those killed was a child while 20 others were injured in Jalalabad city. No group took immediate responsibility.
While the Taliban banned sports like cricket and football in the early years of their rule of Afghanistan, now its fighters enjoy a game of cricket.
A suicide bomber in Afghanistan blew himself on Wednesday in the eastern Afghan city of Jalalabad, an official said.
A suicide attack on protesters in eastern Afghanistan on Tuesday killed at least 68 people, officials said, as an uptick in violence across the country dampens hopes for peace talks and elections.
Gunmen killed 15 in a hostage-taking situation in Jalalabad while a roadside bomb in the western province of Farah hit a passenger bus and killed at least 11 people.
One of the attackers died early in the operation after detonating a suicide bomb but a second held out for several hours before being killed, said a provincial government spokesman.
At least ten were killed and as many wounded after gunmen stormed a government compound in restive Jalalabad city. Meanwhile, Britain is expected to announce sending 440 extra troops to Afghanistan, in a NATO summit.
Daesh claimed responsibility for the attack, with provincial official Sohrab Qaderi saying, "most of the victims were children, who were working in a car wash close to the suicide bombing site."
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