Assessment Questions – Combinatorics

Distinguish novice from competent practitioner:

1. Evaluate the binomial coefficient 6 choose 4.
2. Write a program to evaluate the ratio of (n+1)! to n! and describe the flaws in the resulting output.

Distinguish expert from competent:

1. How can you improve the accuracy of the combinatorical functions without using higher-precision representations?
2. How should you set the boundary between direct evaluation and approximation methods when trying to evaluate combinatorical functions like 4563 choose 4988 ?