The correct option is C Two
Mathematically, the number of restriction sites for a particular endonuclease can be calculated for a given length of DNA by assuming that all four nucleotides are randomly present in equal proportion.
There are four different bases, so probability of finding a particular base at one position will be 14 and frequency of cutting will be 4n, where n is number of base pairs in the recognition sequence. Eco RI recognizes the 6 bp sequence. Hence, there are 46 = 4096 different cleavage site possibilities for given 6 bp recognition sequence.
So, EcoRI will cut once in 4096 base pairs along a DNA. In 10,000 bp DNA fragment, Eco RI will have 100004096 = 2 cleavage sites.