In probability theory, one problem that often arises is determining the number of ways in which...

  

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In probability theory, one problem that often arises is determining the number of ways in which p objects can be selected from a distinct objects without regard to the order in which they are selected. Such selections are called combinations. The number of combinations of p objects from a set with n objects is C (n.p) and is given by: n! C(n. p): (n-p)! p! Write a Python program which will calculate and display on the screen the number of possible combination C based on the values of n and p; where both n and p are positive integers less than 21 and n>p. Implement and use at least the following three functions: fact(...): A function when passed a positive integer value, will calculate and return the factorial of that number. . comb(...): A function when passed n and p (n: total number of objects and p: number of objects taken at a time) will calculate and return the total number of possible combinations (using the formula above). It calls function fact(...) main(...): reads and validates the values of n and p, calls function comb(...) and prints the result. Enter n and p each in range [0,20] and n>p: -8 10 Invalid Input, try again Enter n and p each in range [0,20] and n>p: 5-6 Invalid input, try again Enter n and p each in range [0,20] and n>p: 51 8 Invalid input, try again Enter n and p each in range [0,20] and n>p: 9 17 Invalid input, try again Enter n and p each in range [0,20] and n>p: 86 Number of combinations c(8,6)= 28 Figure 1. Exercise 1 Sample Run In probability theory, one problem that often arises is determining the number of ways in which p objects can be selected from a distinct objects without regard to the order in which they are selected. Such selections are called combinations. The number of combinations of p objects from a set with n objects is C (n.p) and is given by: n! C(n. p): (n-p)! p! Write a Python program which will calculate and display on the screen the number of possible combination C based on the values of n and p; where both n and p are positive integers less than 21 and n>p. Implement and use at least the following three functions: fact(...): A function when passed a positive integer value, will calculate and return the factorial of that number. . comb(...): A function when passed n and p (n: total number of objects and p: number of objects taken at a time) will calculate and return the total number of possible combinations (using the formula above). It calls function fact(...) main(...): reads and validates the values of n and p, calls function comb(...) and prints the result. Enter n and p each in range [0,20] and n>p: -8 10 Invalid Input, try again Enter n and p each in range [0,20] and n>p: 5-6 Invalid input, try again Enter n and p each in range [0,20] and n>p: 51 8 Invalid input, try again Enter n and p each in range [0,20] and n>p: 9 17 Invalid input, try again Enter n and p each in range [0,20] and n>p: 86 Number of combinations c(8,6)= 28 Figure 1. Exercise 1 Sample Run

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