Kenneth Rosen Edition 7 Exercise 8.1 Question 30 (Page No. 512)

Question

• A.  Write out all the ways the product $x_{0} \cdot x_{1} \cdot x_{2} \cdot x_{3} \cdot x_{4}$ can be parenthesized to determine the order of multiplication.
• B. Use the recurrence relation developed in Example $5$ to calculate $C_{4},$ the number of ways to parenthesize the product of five numbers so as to determine the order of multiplication. Verify that you listed the correct number of ways in part $(A).$ 
• C. Check your result in part $(B)$ by finding $C_{4},$ using the closed formula for $C_{n}$ mentioned in the solution of Example $5.$