Brainteaser 1675: The A-to-Z of sport

From The Sunday Times, 16th October 1994 [link]

The individual sport or sports of the 26 members of the Venerable Sports Club means that they are just enough to form:

a football team (11); or
a hockey team (11); or
a rugby team (15).

The number of members playing only two of these sports is the same as the number of members playing rugby only, which is less than one third of the total membership.

How many members play all three sports?

This puzzle was included in the book Brainteasers (2002, edited by Victor Bryant). The puzzle text above is taken from the book.

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