counting

 

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

 

Strap the boys together and consider the pair as a single unit.  With the 3 girs, there are 4 units.     

 

The possible arrangements of 4 units is ₄P₄  =  24 ... but wait, we're not through yet.     

 

Now, have the two boys swap places and there are another 24 arrangements.   

 

So, altogether, there are 48 possible arrangements.     

_.