$(0\mathrm{.}5$ Points$)$ a$.24$ b$.547.$ C$\mathrm{.}14\mathrm{.}4.$ d$\mathrm{.}49\mathrm{.}22.$ Consider the problem of finding the shortest route through several cities, such that each city is visited only once and in the end return to the starting city $($the Travelling Salesman problem$).$ Suppose that in order to solve this problem we use a genetic algorithm, in which genes represent links between pairs of cities. For example, a link between London and Paris is represented by a single gene $$LP$.$ Let also assume that the direction in which we travel is not important, so that LP $=$ P L$.$ a$)$ How many genes will be used in a chromosome of each individual if the number of cities is $10?(0\mathrm{.}5$ Points$)$ b$)$ How many genes will be in the alphabet of the algorithm? $(0\mathrm{.}5$ points$)$