Mel J.

asked • 05/07/21

Combinations Question

A drama club is putting on two plays. There are 11 actors in the Oz play and 7 in the

Grease play.

  1. a) If 3 actors are in both plays, how many actors are there in all?

b) Use a Venn diagram to calculate how many students are only in one of the two plays.


Please explain for each scenario, I don't understand.


1 Expert Answer

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Anthony T. answered • 05/07/21

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I can't draw a Venn diagram here, but I can give you the general idea,


Oz Play both plays Grease play

8 3 4


8 + 3 + 4 = 15


The middle number represents the intersection of the Venn diagram.

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Anthony T.

The Venn diagram would be two intersecting circles. The number that goes in the intersection has to be 3 as that represents the # of actors in both plays. As there are 11 actors in the Oz play, there must be 8 (11-3) that are in the Oz play only. Similarly, as there are 7 in the Grease play, there can only be 4 that are in the Grease play only (7-3). I hope this clears it up for you.
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05/07/21

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