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How can I calculate the following things in my head?

  • $_9C_4$ I know this is $\frac{9\cdot 8\cdot 7\cdot 6}{4\cdot 3\cdot 2\cdot 1}$ and then $3\cdot 2\cdot 3\cdot 7$ but I can't immediately come up with that calculation. Are there some quicker ways do this?

  • $6^5$

  • $68\cdot 27$

I don't want to rely on my calculator anymore. Can anyone give me some mental tricks?

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    It sounds as though you want to be able to compute quickly *in general*, not just for these examples. In this case, there are entire books dedicated to the subject, making your question too broad for this community.2012-08-27
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    @AustinMohr People ask how they can get started in certain areas all the time, or say they've just learned calculus out of some calculus book and ask where they should go next, questions that are much more broad than this, yet do not seem to be too broad for this community.2012-08-27
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    Powers of small integers ($2$ in particular) come up frequently enough to be just memorized. A younger version of yours truly would have done your last example (mental arithmetic only) as: $$68\cdot27=68\cdot30-68\cdot3=2040-204=1836.$$ Multiplying a double digit integer by three is simple enough, and can be reused here.2012-08-27

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