is rugby a type of this game?
No, but both the games originated from a common game.
Rugby football
Rugby football is a collective name for the family of team sports of rugby union and rugby league, as well as the earlier forms of football from which both games, Association football, Australian rules football, and Gridiron football evolved. 
how many premier league titles have man u won Twenty League titles. what is manchester united f.c.? A professional football club . where is the club based in? Old Trafford, Greater Manchester, England. when did the game first begin? The earliest form of the game started during the Han Dynasty (206 BC-220 AD). can you name some associations related to this game? FIFA.
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Rugby football [SEP] Introduction
Rugby football is a collective name for the family of team sports of rugby union and rugby league, as well as the earlier forms of football from which both games, Association football, Australian rules football, and Gridiron football evolved. Canadian football (Grey Cup still has "Rugby Football" written on it), and to a lesser extent American football were also broadly considered forms of rugby football but are seldom now referred to as such. Rugby football started about 1845 at Rugby School in Rugby, Warwickshire, England, although forms of football in which the ball was carried and tossed date to medieval times.