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In a competition of 50 professional ballroom dancers, 22 compete in the fox-..
In a competition of 50 professional ballroom dancers, 22 compete in the fox-trot competition, 18 compete in the tango competition, and 6 compete in both the fox-trot and tango competitions. How many dancers compete in the foxtrot or tango competitions?
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Expert Solution
In a competition of 50 professional ballroom dancers, 22 compete in the fox-trot competition, 18 compete in the tango competition and 6 compete in the both the fox-trot and tango competition
Consider the Addition Principle,
“If one event can occur in m ways and a second event with no common outcomes can occur in n ways, then first or second event can occur in m + n ways.”
6 dancers compete in the both the fox-trot and tango competition. Hence, 6 will be subtracted from the sum of number of dancers who compete in the fox-trot competition and the number of dancers who compete in the tango competition.
That is, the number of dancers who compete in the fox-trot or tango competition will be equal to the “number of dancers who compete in the fox-trot competition” plus “number of dancers who compete in the tango competition” minus 6.
22 + 18 – 6 = 34
Therefore, the number of dancers who compete in the fox-trot or tango competition will be 34.
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