4.6: Counting Rules

Question 1

What is the counting rule for multiple-step experiments?

Answer 1

For an experiment of k steps with n1, n2, …, nk possible outcomes at each step, the total number of experimental outcomes is the product n1(n2)…(nk).

Question 2

How many total outcomes are there for a three-question true/false quiz?

Answer 2

There are 2^3 = 8 total outcomes for a three-question quiz, representing all combinations of correct (C) and incorrect (I) answers.

Question 3

What is the formula for the number of combinations of n items from N items?

Answer 3

The number of combinations is denoted as (N choose n) and calculated using the formula:

N! / [n!(N - n)!].

Question 4

What is the probability of winning the lottery by selecting 6 numbers from 47?

Answer 4

With (47 choose 6) combinations, the probability of winning by selecting 6 numbers is 1 / 10,737,573.