How to calculate possible number of allele combination in given genotype?

Combination of alleles in any organims is known as its genotype. An allele is one of two or more alternate forms of a gene located at the corresponding locus on homologous chromosome. One allele obtained from the mother and the other from the father. Any possible combination of alleles is possible for the individuals within a particular population. If three alleles, A, B, and C are present on any specific locus, there will be six genotypes possible. An individual with above alleles may have any of the following allele combinations: AA, AB, AC, BB, BC and CC.

The number of possible genotypes or possible combination of alleles can be calculated by two methods. 

(1) It can be calculated by adding the number of possible combination of alleles with each positive integer below that number. For example, for a locus having three possible alleles, the number of possible genotypes is                                              3+2+1= 6

(2) The number of possible combination of alleles can also be calculated by using following formula
Number of allele combination = n(n+1)/2

Where, n is equal to the number of possible alleles.Here, number of alleles are 3,Therefore,
                                     3(3+1)/2 = 12/2=6

From above discussion, we can say that there are six possible allele combination occur if any individual have three alleles.

Problem:  There are 15 different alleles are present at a VNTR (variable number of tandem repeats) locus. How many combination of alleles (genotypes) are possible in a population for this VNTR?Explanation:
We can calculate by using both aforementioned methods

          (1)     15+14+13+12+11+10+9+8+7+6+5+4+3+2+1= 120

          (2)     By the use of formula
     Number of allele combination =15(15+1)/2=(15)(16)/2=240/2                                                                               =120

Therefore, for a locus having 15 different alleles, 120 different allele combination or genotypes are possible.