How many strings of five characters use the letters a, b, c, d and do not have the letters bad appearing consecutively and in this order? (Letters can occur any number of times, including not at all.)
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Hint: abad, bbad, cbad, dbad, bada, badb, badc, badd – Theo Douvropoulos Apr 10 '15 at 03:31
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@Theo what are you doing? huh? – RE60K Apr 10 '15 at 04:47
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@ADG Oh, I'm sorry, these are all the bad 4-character strings... Well, you get the idea for five as well... Then subtract those from the $4^5$ possible strings and you are set... – Theo Douvropoulos Apr 10 '15 at 05:43
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Total $= 4^5$
Strings containing bad $\newcommand{\1}[2]{{}^{#1}{\mathbb C}_{#2}}= \1314^2$
Subtract those.
N. F. Taussig
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RE60K
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The strings you eliminated have length $6$. They should have length $5$. – N. F. Taussig Apr 10 '15 at 11:38
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