My instructor wrote
$$\binom{n}{k}=\binom{n}{k-1}-\binom{n-1}{k-1}$$
I doubt it is incorrect.
Is it?
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3$\begingroup$ Just try some numbers, and you'll see? $\endgroup$– Hans LundmarkCommented Jun 20, 2017 at 16:27
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1$\begingroup$ That won't establish that it's correct. $\endgroup$– Shaun ♦Commented Jun 20, 2017 at 16:28
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3$\begingroup$ @Shaun Yes, but it will establish it if it is incorrect. $\endgroup$– projectilemotionCommented Jun 20, 2017 at 16:29
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2$\begingroup$ It might be good to say why you doubt it's correct (unless you're skeptical of everything your professor writes) -- did you see a different formula elsewhere? Did you try an example that didn't work? Edit: although now I see you "doubt it is incorrect", so the whole thing is odd. $\endgroup$– pjs36Commented Jun 20, 2017 at 16:33
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1$\begingroup$ I am wondering if your prof meant to write something like. $\binom{n}{k}=\binom{n-1}{k-1}+\binom{n-1}{k}$ $\endgroup$– Doug MCommented Jun 20, 2017 at 16:58
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2 Answers
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$$3=\binom{3}{2}\neq\binom31-\binom21=3-2=1$$
answered Jun 20, 2017 at 16:48
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Search Pascal's rule , i think your assumption is wrong. https://en.wikipedia.org/wiki/Pascal%27s_rule
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1$\begingroup$ thank you so much , i didn't know anything , i couldn't even write the answer. $\endgroup$ Commented Jun 21, 2017 at 15:39