<PRE><B>Question 1030955</B>
An art gallery has a total of 11 paintings by a particular artist; of these, 5 are oil paintings and 6 are water colour paintings. The art gallery is asked to provide a special exhibition of this artist’s work but is restricted to showing only five of the paintings. Calculate the number ways in which the five paintings can be selected for the exhibition if :

a.there are no restrictions:: 11C5 = 462 selections
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b.one particular painting must be included:: 1*10C4 = 210 selections
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c.there must be exactly three watercolour paintings::6C3*5C2
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d.there must be more watercolour paintings than oil paintings::6C3*5C2+6C4+5C1+6C5
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Cheers,
Stan H.
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