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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?

 Jun 1, 2022
 #1
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+1

 

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

 

B1B2  G1  G2  G3        G1  B1B2  G2  G3        G1  G2  B1B2  G3        G1  G2  G3  B1B2 

B1B2  G1  G3  G2        G1  B1B2  G3  G2        G1  G3  B1B2  G2        G1  G3  G2  B1B2 

B1B2  G2  G1  G3        G2  B1B2  G1  G3        G2  G1  B1B2  G3        G2  G1  G3  B1B2 

B1B2  G2  G3  G1        G2  B1B2  G3  G1        G2  G3  B1B2  G1        G2  G3  G1  B1B2 

B1B2  G3  G1  G2        G3  B1B2  G1  G2        G3  G1  B1B2  G2        G3  G1  G2  B1B2 

B1B2  G3  G2  G1        G3  B1B2  G2  G1        G3  G2  B1B2  G1        G3  G2  G1  B1B2 

 

So far, we've found 24 ways to arrange these people, with the boys standing Boy 1 Boy 2. 

Now change the position of the boys, to B2B1, and do the same thing for another 24 ways. 

 

Total possible arrangements, 48 ways.  

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 Jun 1, 2022
 #2
avatar+117494 
+1

Tie the 2 boys together

 

2*4! = 48

 

I multipled by 2 because they can be in 2 orders    B1 B2  or  B2 B1

 Jun 1, 2022
edited by Melody  Jun 1, 2022

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