AppliedMultiple choice

What does $k\binom{n}{k} = n\binom{n-1}{k-1}$ say, in words?

ABoth sides count a committee of $k$ with a chair
BIt is Pascal’s rule written in a different arrangement
CIt is the symmetry relation between $k$ and $n-k$
DIt holds only when $k$ divides $n$ exactly

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Binomial identities, and proving them by counting twice

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What does k(nk)=n(n−1k−1)k\binom{n}{k} = n\binom{n-1}{k-1}k(kn​)=n(k−1n−1​) say, in words?

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