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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?

 Aug 4, 2021
 #1
avatar+34380 
+3

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gggbb         four ways for the two boys......but the two boys could switch places making 8 ways for the boys to be in line

                        then the other three spots can be filled by the girls   3 x 2 x 1    6 ways

 

8 x 6 = 48 ways    (this assumes the boys and girls are distiguishable)

 Aug 4, 2021
 #2
avatar+114511 
+2

If you want to assume that the children are not identical then you tie the boys together and not you have 4 'children'

they can be arranged in a line in 4! ways.  But either one of the boys can be to the left so we need to double this answer.

 

4!*2 = 48 ways

 Aug 4, 2021

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