a) A DNA sequence is made up of four bases: A, T, C, and G. If a 4-element DNA sequence does not contain the base T, it can only contain the bases A, C, and G. Each position in the sequence can be one of these three bases, so there are 3 options for each of the 4 positions. Therefore, there are 3^4 = 81 such sequences.

b) If a 4-element DNA sequence must contain the sequence ACG, then those three bases must be in that order. There is only one position left, which can be any of the four bases. Therefore, there are 4^1 = 4 such sequences.

c) If a 4-element DNA sequence must contain all four bases A, T, C, and G, then each base must appear exactly once. The number of such sequences is the number of permutations of 4 elements, which is 4! = 24.

d) If a 4-element DNA sequence must contain exactly three of the four bases, then one base is missing and one base appears twice. There are 4 options for which base is missing, and then 3 options for which of the remaining bases appears twice. The two identical bases can be in any 2 of the 4 positions, and the other two bases can be in any order in the remaining positions. Therefore, there are 4 * 3 * (4 choose 2) * 2 = 144 such sequences.

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a) A DNA sequence is made up of four bases: A, T, C, and G. If a 4-element DNA sequence does not contain the base T, it can only contain the bases A, C, and G. Each position in the sequence can be one of these three bases, so there are 3 options for each of the 4 positions. Therefore, there are 3^4 = 81 such sequences.

b) If a 4-element DNA sequence must contain the sequence ACG, then those three bases must be in that order. There is only one position left, which can be any of the four bases. Therefore, there are 4^1 = 4 such sequences.

c) If a 4-element DNA sequence must contain all four bases A, T, C, and G, then each base must appear exactly once. The number of such sequences is the number of permutations of 4 elements, which is 4! = 24.

d) If a 4-element DNA sequence must contain exactly three of the four bases, then one base is missing and one base appears twice. There are 4 options for which base is missing, and then 3 options for which of the remaining bases appears twice. The two identical bases can be in any 2 of the 4 positions, and the other two bases can be in any order in the remaining positions. Therefore, there are 4 * 3 * (4 choose 2) * 2 = 144 such sequences.

Knowee AI · Accepted Answer

a) A DNA sequence is made up of four bases: A, T, C, and G. If a 4-element DNA sequence does not contain the base T, it can only contain the bases A, C, and G. Each position in the sequence can be one of these three bases, so there are 3 options for each of the 4 positions. Therefore, there are 3^4 = 81 such sequences.

b) If a 4-element DNA sequence must contain the sequence ACG, then those three bases must be in that order. There is only one position left, which can be any of the four bases. Therefore, there are 4^1 = 4 such sequences.

c) If a 4-element DNA sequence must contain all four bases A, T, C, and G, then each base must appear exactly once. The number of such sequences is the number of permutations of 4 elements, which is 4! = 24.

d) If a 4-element DNA sequence must contain exactly three of the four bases, then one base is missing and one base appears twice. There are 4 options for which base is missing, and then 3 options for which of the remaining bases appears twice. The two identical bases can be in any 2 of the 4 positions, and the other two bases can be in any order in the remaining positions. Therefore, there are 4 * 3 * (4 choose 2) * 2 = 144 such sequences.

(7 POINTS) How many 4-element DNA sequencesa) (1 POINT) do not contain the base T?b) (2 POINTS) contain the sequence ACG?c) (2 POINTS) contain all four bases A, T, C, and G?d) (2 POINTS) contain exactly three of the four bases A, T, C, and G?

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