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DOWNLOAD Autodesk Robot Structural Analysis Professional 2010 Multilingual X86 DVDrar. Recently added the video to my website and it is completely free for watching .Q:

How many ways can $4$ children of $10$ children of $8$ children of $6$ children be arranged in a row such that all are boys or all are girls?

This one I had to think about for so long and I am still not sure if it’s right answer. Here is how I approached the problem:

$$4\binom{10}{4}\cdot2\binom{8}{4}\cdot2\binom{6}{4}$$

I am not sure if it’s correct because it feels like I am missing something. What I am missing and how can it be corrected?

A:

Your answer is correct. The problem with your reasoning is that you haven’t counted the permutation that has two girls and two boys, while the correct answer is four times your answer.
You could also do it as follows: $${4\choose 2}\cdot{6\choose 4}\cdot{10\choose 4}$$

A:

Instead of the straightforward way,
Look at the children of the four boys,
firstly a boy, then one of the 4 girls, then a boy and one of the four girls,
then a boy again and the other boy, and so on…
there are in fact $$4\binom{4}{2}\cdot

].

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