1. Binomial Formula

3. There is a Formula for Finding the Number of Orderings - involves FACTORIALS

4. k! = k(k - 1)(k - 2)...(3)(2)(1) “k factorial” 4! = 4 x 3 x 2 x 1 = 24 3! = 3 x 2 x 1 = 6 1! = 1 0! = 1 Factorial

5. Formula for Number of Orderings If there are n objects of which... k are alike of one kind n - k are alike of another kind the number of ways these objects can be arranged in a row is given by Binomial Coefficients Note:(n - k)! = (n - k)(n - k - 1)...(3)(2)(1) (n - k)! = n! - k! n! k!(n - k)! }

7. Binomial Assumptions Chance situation (“trial”) repeated a fixed number (n) of times Requirements: l Only 2 possible outcomes per trial (“success” and “failure”) l Probability of “success” stays constant across trials Notation: p = Pr[“success”] on each trial 1 - p = Pr[“failure”] on each trial l Trials are independent

8. Binomial Distribution The probability of k successes out of the n trials is Number of orderings resulting in k successes Probability of each ordering that results in k successes P(k) = n! k!(n - k)! p k (1 - p) n - k