Uma secretária possui 6 camisas, 4 saias, e 3 pares de sapatos. Qual o número de maneiras distintas com que a secretária poderá
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You can try to show this by induction:
• According to the given closed form, we have , which agrees with the initial value <em>S</em>₁ = 1.
• Assume the closed form is correct for all <em>n</em> up to <em>n</em> = <em>k</em>. In particular, we assume
and
We want to then use this assumption to show the closed form is correct for <em>n</em> = <em>k</em> + 1, or
From the given recurrence, we know
so that
which is what we needed. QED