35) There are 12 boys and 16 girls in one class, and 15 boys and 14 girls in another. How many ways can a boy-girl pair be chosen, if the boy has to be from one class and the girl from the other?
The only condition is that the boy and the girl must be from different classes.
Class 1 - 12 boys and 16 girls
Class 2 - 15 boys and 14 girls
You can do it in 2 ways: Pick a boy from Class 1 and girl from class 2 OR pick a girl from class 1 and boy from class 2.
Number of ways of picking a boy from Class 1 and girl from class 2 = 12*14
Number of ways of picking a girl from class 1 and boy from class 2 = 16*15
Total number of ways = 12*14 + 16*15
We are just using the basic counting principle here. Check this link for more: http://www.veritasprep.com/blog/2011/10 ... inatorics/
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