Roberta is lining up nine different coloured blocks. There are five green blocks, two white blocks and two orange blocks. In how many ways can she arrange these blocks?

Respuesta :

AL2006
If the blocks were 9 different colors, then there would be

     9 !(factorial) = 362,880 different ways to line them up.

But for each different line-up, there are 5! =120 ways to arrange
the green blocks and you can't tell these apart, 2!= 2 ways to arrange
the white blocks and you can't tell these apart, and 2!=2 ways to arrange
the orange blocks and you can't tell these apart.

So the number of distinct, recognizable ways to arrange all 9 blocks
is

         (9!) / (5! · 2! · 2!)  =  (362,880) / (120 · 2 · 2)  =  756 ways.