Prompt Title: Binomial Coefficients Formula.

Here's a Python program that uses the binomial coefficients formula to calculate the number of ways to choose r items from a set of n items:

pythonCopy code
import math

# Get input values for n and r
n = int(input("Enter the size of the number field (n): "))
r = int(input("Enter the pick size (r): "))

# Calculate the binomial coefficient using the formula
coeff = math.factorial(n) // (math.factorial(r) * math.factorial(n - r))

# Print the result
print("The number of ways to choose {} items from a set of {} items is {}".format(r, n, coeff))

In this program, we use the math module to access the factorial function, which is used to calculate the factorials of n, r, and n-r that appear in the binomial coefficients formula. We use the double slash (//) operator to perform integer division, which ensures that the result is a whole number. Finally, we use format method to print out the result with appropriate formatting.