combinatorics

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Question

combinatorics

a. How many 16 letter strings can be made from the letters a, b or c?

b. How many 16 digit sequence with 4 a’a, 7 b’s and 5 c’s are there

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Answer 1

Answer #1

a) 3 choices for the first letter, 3 choices for the second letter, 3 choices for the third letter, and so on. Therefore total no of 16 - letter strings that can be made from the letters a, b, or c is \(3^{16}\).

answered by: studyres

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Answer 2

Answer #2

b) We have 16 choices for first letter, 15 choices for second letter, 14 choices for third letter and so on. since the letters are being repeated, so total no. of \(16-\) letter strings that can be made from \(3 \mathrm{a}^{\prime} \mathrm{s}, 6 \mathrm{~b}^{\prime} \mathrm{s},\) and \(7 \mathrm{c}^{\prime} \mathrm{s}\) are \(\frac{16 !}{4 ! 7 ! 5 !}\)

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Answer 3

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