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Consider the statement

In an appliance repair shop, the following are found $10$ televisions for repair, of which $3$ are of brand $A$, $3$ of brand $B$ and $4$ of brand $C$. The order in which the televisions are repaired is random.

I want to find the probability $P_{1}$ that the order of repair of the TV sets is $CABCABCABC$

Naturally, there are $10!$ ways to repair $10$ televisions considering order, but my question is about how to find the number of ways to accommodate the pattern $CABCABCABC$

Any help to solve the doubt? thank you!

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    $\begingroup$ A general technique to answer questions like this -- one that gives a simple formula you can immediately write down without any computation -- is described at stats.stackexchange.com/a/415878/919. $\endgroup$
    – whuber
    Feb 26 at 15:19

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