a. Determine the number of k-faces of the 5-dimensional simplex S 5 for k = 0,1, .........,

Question:

a. Determine the number of k-faces of the 5-dimensional simplex S⁵for k = 0,1, ^.........,4. Verify that your answer satisfies Euler’s formula.
b. Make a chart of the values of f_k(Sⁿ) for n = 1,........,5 and k = 0,1,.........,4. Can you see a pattern? Guess a general formula for f_k(Sⁿ).