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Counting problem

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How many ways can you arrange 2 boys and 3 girls in a line, if the 2 boys must stand next to each other?

Jan 22, 2022

#1
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A common stratergy you can use to tackle these problems is to treat the two boys, as a single person, and then just count the possible ways to arrange the people.

Lets think of these 2 boys, as a single person. Then, there are 4! ways to arrange the single person, and the 3 other girls in a line.

There is also usually a mistake made, because the two people mixed in as a single person, can also be re-arranged.

4! * 2! = 48

This problem is similar to the AMC 8 2020 #10 problem.

You can view the problem here:

https://artofproblemsolving.com/wiki/index.php/2020_AMC_8_Problems/Problem_10

Jan 22, 2022
#2
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Consider.     (BB)     G     (BB)         G      (BB)        G     (BB)

The 2 boys can occupy 4 spaces as shown above.

There are 4 ways to place that group of boys in the line, 4!= 24. 3!=6 ways of arranging the girls after that and 2!=2 ways of arranging the boys within their cluster, so the answer must be 2×4!×3!=2x24x6 = 288.

Jan 22, 2022