Doubt regarding choice of formula...

Both the techniques are correct , we can help u by giving an example ,

Lets say u have to calculate probability of an event where a dice is tossed thrice , number 6 appears only once .

 

The above problem can have sample spaces { 6 , not 6 , not 6 } , {not 6 , 6 , not 6} , {not 6 , not 6 , 6}

So probability =  3 * 1/6 * 5/6 * 5/6

But we can also say that out of the three probabilities 2 are same 5/6

So answer can be

1/6 * 5/6 * 5/6 * 3C₂