What is the solution to this mathematics competition question?

[blade007]

I have a mathematics competition next month. I was doing these last year sample questions and got stuck at this one. Can anyone please help me out? Much appreciated.

This is the question -

Six hundred and sixty six students sit for a prestigious mathematics contest. It is known that all of the students who sit the exam attend an all girls school and/or play sport on the weekend, and/or play a musical instrument. One hundred and eleven of the students attend an all girls school and two hundred and twenty two attend an all boys school. Four hundred and forty four of the students play musical instruments and five hundred and fifty five of the students play sport on the weekend. Seventy seven of the students attend an all girls school and play sport on the weekend. Eighty eight of the students attend an all girls school and play a musical instrument. Three hundred and thirty three of the students play a musical instrument and play sport on the weekend. Of the students who attend an all boys school thirty three do not both play sport on the weekend and play a musical instrument. How many of the students attend a co-ed school, play sport on the weekend and play a musical instrument?

 

[micromass]

Check this out: http://en.wikipedia.org/wiki/Inclusion-exclusion_principle