Combinations: building three towers with nine blocks

[Peter6384]

We have nine wooden blocks, with all the blocks being different size. We want to build three towers in a row, each made from three blocks, so that in each tower the size of the cubes from below decrease upwards. How many different triplets of towers like this can we make if the order of towers matters.
(official answer is 1680 but i dont know the way to solve it)

 

[blamocur]

How many ways are there to pick the blocks for the first tower?

 

[pka]

We have nine wooden blocks, with all the blocks being different size. We want to build three towers in a row, each made from three blocks, so that in each tower the size of the cubes from below decrease upwards. How many different triplets of towers like this can we make if the order of towers matters.
(official answer is 1680 but i dont know the way to solve it)

PLEASE Explain why [imath]\large{\bf{\dbinom{9}{3}\cdot\dbinom{6}{3}=?}}[/imath] actually solve this question!

[imath][/imath]

 

[Peter6384]

PLEASE Explain why [imath]\large{\bf{\dbinom{9}{3}\cdot\dbinom{6}{3}=?}}[/imath] actually solve this question!

[imath][/imath]

Oh, thank you so much, I was stuck with picking blocks where one has to be bigger than the others, I didn't realize that if you pick 3blocks you can always put them in a tower with decreasing size. Thanks, I get it now.