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5. Ternary strings. A ternary string is a word from the alphabet {0,1,2}{0,1,2}. For example, 022101022101...

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Advance Math

5. Ternary strings. A ternary string is a wordfrom the alphabet {0,1,2}{0,1,2}. For example, 022101022101 is aternary string of length 6.

(a) Enumerate all ternary strings of length 2.
(b) Generalize: how many ternary strings have length r?
(c) A ternary string of length 6 is to be made. How many ways canwe choose how many 0's, 1's, and 2's to include in thestring?
(d) A ternary string of length 6 is to have two 0's, a 1, and three2's. How many strings have this property?
(e) What is the probability that a ternary string of length 6 hastwo 0's, a 1, and three 2's?

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