Computing probability of $k$ errors in a $q$-ary repetition code over a symmetric channel

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I'm reading up on some coding theory and I'm having a hard time understanding error probabilities in $q$-ary repetition codes. Particularly, what I'm lost on conceptually is how to solve problems of the following type:

A $q$-ary repetition code is transmitted in a symmetric channel, with some probability $p$ that there will be a symbol error. What is the probability that there will be $k < q$ or more errors in transmitting a codeword?

I've seen formulas for specific examples with defined $q$, $k$, and $p$, but can't really wrap my head around the general approach to a problem like this.