DNA sequencing is the workhorse of modern biology and medical studies . Its goal is to determine the order of nucleotides on a DNA sequence . The most popular approach , shotgun sequencing , is made up of two major parts : first cutting the sequence into pieces and reading them by a sequencing machine , and then putting the reads together and reconstructing the sequence by an assembler . Significant theoretical studies on sequencing problem have always pursued the goal of getting a unique sequence at the output of the assembler; otherwise the sequencing procedure would be considered as a failure . As this approach seems to be too strict , in this thesis we propose a new criterion . For each sequence , we consider the number of possible sequences at the output of the assembler and introduce the average of this number as a criterion for evaluating the sequencing procedure . First we present a combinatorial model for calculating the probability of having arbitrary number of equations of arbitrary elements of a random sequence . Then using this model , we calculate the probability of having a pair of leftmost interleaved repeats in a sequence . Defining the concept of compatibility of a sequence with a read set and considering the L-spectrum of the sequences , we find a lower bound on the average of the number of compatible sequences . Finally , by presenting the results of computations , we provide some conjectures on the behavior of the average of the number of compatible sequences and the number of different spectrums with respect to sequence length and read length . Key Words: DNA - Shotgun sequencing - de novo - assembly