Most binomial probability calculations required in these exercises can be done by using Table C or the Normal approximation. Your instructor may request that you use the binomial probability formula or software. In exercises requiring the Normal approximation, you should use the continuity correction if you studied that topic.

Question 5.36

5.36 Show that these facts are true.

Use the definition of binomial coefficients to show that each of the following facts is true. Then restate each fact in words in terms of the number of ways that successes can be distributed among observations.

  1. for any whole number .
  2. for any whole number .
  3. for any whole number .
  4. for any whole numbers and with .