Question

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?

Answer 1

This is the concept of permutations, to get the number of different colour patterns obtained when 5 identical red wooden blocks and 6 identical wooded blocks stacked together, we calculate for their permutations which is:
6P5
=720
the answer is 720 patterns

Answer 2

Answer:

462

Step-by-step explanation:

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 $5+6=11$ blocks. And number of ways to arrange 11 blocks would simply be: $11!$.

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

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

$\frac{\text {ways all blocks can be stacked}}{\text{ways red blocks can be stacked} \times \text{ways white blocks can be stacked}}$

So in this case it is:

$=\frac{11!}{5! \times 6!} =462$

Therefore, there could be 462 colour patterns.