Computing the number of possibilities. Fundamental Counting Theorem: If there are separate events, multiply the number of choices of each. For example, when making a meat and cheese sandwich, the number of possible combinations depends on the number of choices of meat and the number of choices of cheese. If there's one type of meat and three types of cheese, there's a total of three sandwiches ( 1 x 3 = 3). If there are four types of meat and three types of cheeses, there are twelve possibilities (3 x 4). Permutations: If order makes a difference, multiply the number of choices for the first position by the number of choices left for the second position, continuing to multiply by the possibilities for each position until all positions are filled. n For example, if you are choosing a president and vice president from a group of 30, there are 30 possibilities for president and 29 possibilities for vice president (30 x 29), giving 870 total possibilities. Combinations: If order doesn't make a difference (think of pizza...is a sausage hamburger pizza the same as a hamburger sausage pizza?), multiply like permutations, but then divide by the factorial of the number of items being taken. For example, if a committee is to consist of three members and there are 8 people from whom to choose. (8 x 7 x 6 = 336 divided by 3 x 2 x 1 = 6 giving a total of 56 possible committees)
Probability is defined as the total number of success over the total number of possible outcomes.
Computing the number of possibilities.
Fundamental Counting Theorem: If there are separate events, multiply the number of choices of each. For example, when making a meat and cheese sandwich, the number of possible combinations depends on the number of choices of meat and the number of choices of cheese. If there's one type of meat and three types of cheese, there's a total of three sandwiches ( 1 x 3 = 3). If there are four types of meat and three types of cheeses, there are twelve possibilities (3 x 4).
Permutations: If order makes a difference, multiply the number of choices for the first position by the number of choices left for the second position, continuing to multiply by the possibilities for each position until all positions are filled. n For example, if you are choosing a president and vice president from a group of 30, there are 30 possibilities for president and 29 possibilities for vice president (30 x 29), giving 870 total possibilities.
Combinations: If order doesn't make a difference (think of pizza...is a sausage hamburger pizza the same as a hamburger sausage pizza?), multiply like permutations, but then divide by the factorial of the number of items being taken. For example, if a committee is to consist of three members and there are 8 people from whom to choose. (8 x 7 x 6 = 336 divided by 3 x 2 x 1 = 6 giving a total of 56 possible committees)
Probability is defined as the total number of success over the total number of possible outcomes.
Check your knowledge at Combinations & Permutations Quiz and Permutations and Combinations Practice
Further information and practice at Counting Principle,
Explore a variety of probability events.