Question

How many 5-element DNA sequences

a) end with A?

b) start with T and end with G?

c) contain only A and T?

d) do not contain C?

Hint: Recall that a DNA sequence is a sequence of letters, each of which is one of A, C, G, or T. Thus by the product

rule there are 4^5 = 1024 DNA sequences of length five if we impose no restrictions.

discrete strctures

Answer 1

a) Number of elements ending with A means that only the first 4 elements can be changed and the last element has to A. So total such number of elements = 4^4 = 256.

b) Number of elements that start with T and end with G means that only thr middle 3 elements can be changed. So the total such number of elements = 4^3 = 64.

c) Number of elements that contain only A and T means that we have only 2 options to fill all the 5 elements. So total such number of elements = 2^5 = 32.

d) Number of elements that do not contain C means that we have only 3 letters to choose from, to make the elements of the DNA sequence. So total such number of cases = 3^5 = 243.

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