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In a class there are 12 boys and 7 girls...

In a class there are 12 boys and 7 girls. The teacher wants to select either a boy or a girl to represent the class in a competition. In how many ways can the teacher make this selection.

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The teacher has to perform two jobs
(i) Selecting a boy among 12 boys and
(ii) Selecting a girl among 7 girls
The first can be performed in 12 ways and the second in 7 ways .
Hnece, either a boy or girl can be selected for a competition in 12+7=19 ways.
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