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?

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.