Why don't we have more elements? By looking at the number of subatomic particles there seem to exist, there should be thousands of element configuration combinations possible. But we have found just over hundred elements to exist. What is the explanation for this?
 A: The term "element" is reserved for atoms that have a nucleus that is a combinations of at least one proton and optionally one or more neutrons.  
Also, only a difference in the number of protons makes a nucleus considered that of a different element.  Changing just the number of neutrons only makes a different isotope.  Changing the number of electrons is considerd a different ionization state of the same element. 
Muonic hydrogen, where the eletron is replaced by a muon, is not considered a new element.  
Hypernuclei, where lamba or sigma particles are added to a nucleus, are referred to as isotopes rather than new elements.
A: The nucleus obeys quantum mechanical laws. It is not the number of combinations that controls the existence of an element (or an isotope of the element) but the number of solutions of the specific quantum mechanical equation that describes the nucleus. This is a many body problem and has been approached by quantum mechanical models as the shell model, which uses an effective potential well to get at the allowed energy levels for a conglomerate of nucleons, protons and neutrons.
Two factors contribute to the potential, the spill over strong force from the bound quarks within the proton and neutron, and the repulsion from the electric field of the same charge protons. Qualitatively the neutrons  help to shield the repulsive proton-proton force so as to allow the attraction of the strong force to create the potential well. This interplay is responsible for the large number of neutrons for high Z nuclei: the more protons there are the  higher the quantum mechanical probability of their neighboring  to another proton, and the more shielding from neutrons needed. 
As the number of necessary neutralizing neutrons grows, a third factor becomes dominant: neutrons are unstable  when free and decay with beta decay. There can exist a quantum mechanical probability for this decay even in low Z nuclei.. This decay probability is very large when the number of neutrons becomes large. This is true for other decay modes, for alpha particle for example, in nuclei with too many protons or neutrons the probabilities of instability  become large as is seen in the figure, where the black entries are stable.
So the combinations are limited by the quantum mechanical dynamics.
A: The reason the number of elements is finite is because of the proton electric charge.  For larger atoms the electromagnetic repulsion between protons eventually overcomes the nuclear binding from the strong force and the nuclei become unstable.
A: Well the short answer is as the larger the nucleus becomes, the more unstable it is, and it is liable to fall apart (in the form of radiation). So that is why uranium, an element with a large nucleus is used in nuclear fission because it is easier to decay over an element such as iron. This is basically what limits the elements to 118 natural elements. Although scientists have created other larger elements, their half-lives are very short so they don't stick around very long.
