Suppose that 5 identical red wooden blocks and 6 identical white wooden blocks are to be stacked, one on top of another, to form one tall tower of blocks. How many different colour patterns can result?

Firstly, we will calculate the number of ways we can arrange total number of wooden blocks. Lets say each of them are independent, so altogether we have [tex]5+6=11[/tex] blocks. And number of ways to arrange 11 blocks would simply be: [tex]11![/tex].

Now, we need to figure out the number of ways 5 red wooden blocks can be arranged, it is [tex]5![/tex] and the number of ways 6 white wooden blocks can be arranged is [tex]6![/tex]. These are the ways they can be arranged in themselves.

So, we can now find how many different colour patterns can result by:

[tex]\frac{\text {ways all blocks can be stacked}}{\text{ways red blocks can be stacked} \times \text{ways white blocks can be stacked}}[/tex]

So in this case it is:

[tex]=\frac{11!}{5! \times 6!} =462[/tex]

Therefore, there could be 462 colour patterns.

Suppose that 5 identical red wooden blocks and 6 identical white wooden blocks are to be​ stacked, one on top of​ another, to form one tall tower of blocks. How many different colour patterns can​ result?

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Suppose that 5 identical red wooden blocks and 6 identical white wooden blocks are to be stacked, one on top of another, to form one tall tower of blocks. How many different colour patterns can result?