(a) An unordered list of 20 cars is a combination of 20 cars from this car dealership where the order does not matter, that is to say that if two lists include the same 20 cars they are considered to be the same unordered lists. How many unordered lists of 20 cars can be created in which no car is displayed more than once?

We as humans write math expression in infix notation, e.g. 5 + 2 (the operators are written in-between the operands). in a computer’s language, however, it is preferred to have the operators on the right side of the operands, i.e. 5 2 +. for more complex expressions that include parenthesis and multiple operators, a compiler has to convert the expression into postfix first and then evaluate the resulting postfix.write a program that takes an “infix” expression as input, uses stacks to convert it into postfix expression, and finally evaluates it. it must support the following operations: + - / * ^ % (example infix expression: (7 - 3) / (2 + 2)postfix expression: 7 3 - 2 2 + /result: 1guidelines: 1. you will need to use stacks in three placesa. one for the parenthesis check [char stack]b. one during infix to postfix [char stack]c. one during evaluation [int stack]for a and b above, you can use same array and same push, pop method as both ofthem are char. but for evaluation you have int stack and you might consider to createanother push pop method to handle it. maybe push_int, pop_int, etc. or find otherstrategy to utilize existing push pop method2. you can create a function for obtaining operator priority. that function should take anoperator as input and return its priority as an integer. this function will you a lot andreduce repeated code3. during evaluation you will need to convert char into integer. example for single digit: char c = '5'; int x = c - '0';

Consider the following statements: struct nametype{string first; string last; }; struct coursetype{string name; int callnum; int credits; char grade; }; struct studenttype{nametype name; double gpa; coursetype course; }; studenttype student; studenttype classlist[100]; coursetype course; nametype name; mark the following statements as valid or invalid. if a statement is invalid, explain why.a.) student.course.callnum = "csc230"; b.) cin > > student.name; c.) classlist[0] = name; d.) classlist[1].gpa = 3.45; e.) name = classlist[15].name; f.) student.name = name; g.) cout < < classlist[10] < < endl; h.) for (int j = 0; j < 100; j++)classlist[j].name = name; i.) classlist.course.credits = 3; j.) course = studenttype.course;

Write a method that takes in an array of point2d objects, and then analyzes the dataset to find points that are close together. be sure to review the point2d api. in your method, if the distance between any pair of points is less than 10, display the distance and the (x,y)s of each point. for example, "the distance between (3,5) and (8,9) is 6.40312." the complete api for the point2d adt may be viewed at ~pf/sedgewick-wayne/algs4/documentation/point2d.html (links to an external site.)links to an external site.. try to write your program directly from the api - do not review the adt's source code.