Why? Because, for one of these locks, the correct "combination" isĭetermined not only by the numbers that are selected, but also by the order in Poor choice of words: the device that we commonly call a combination lock would more accurately be called a permutation lock or a fundamental How many outcomes are possible under this new scheme? Now, the Lotto works like this: there are 53 balls instead of 49. How many different outcomes are possible? If the numbers on the ping-pong balls match The machine randomly spits out 6 ping-pong balls. There are 49 ping-pong balls in a machine, each bearing a number from 1 to 49. The Florida Lotto Saturday night drawing used to work like this: (assuming that no topping can be repeated on a pizza)?ĮXAMPLE 1.5.15 Classic example of combinations How many different 4-topping combinations are possible The choices for toppings are pepperoni, sausage, olives, mushrooms, anchovies, peppers, and onions. How many different three-dog groups are possible?Ī pizzeria is offering a special: for $6 you get a four-topping pizza. New question: After the race, three dogs will be randomly chosen for veterinary examination. Orders of finish are possible? We saw that the answer was P(6,3) = 120. ![]() Race: Spot, Fido, Bowser, Mack, Tuffy, William. Recall this problem from earlier: There are six greyhounds in a The password for Gomer's e-mail account consists of 5 characters chosen from the set How many different orders of finish (first place through eighth place) are possible?ġ. In how many ways is it possible for 15 students to arrange themselves among 15 seats Choose third-strongest candidate: 2 optionsĪ shorter way to get this answer is to recognize that the problem isĪsking us to find the number of ways to arrange (according to relative suitability) four people.īy definition, the number of ways to arrange 4 things is 4! Choose second-strongest candidate: 3 optionsģ. If you were to use the Fundamental Counting Principle, you would need to make four dependent decisions:Ģ. Rank the four candidates from strongest to weakest. N! is the number of different ways to arrange ( permutations of) n objects. N! is n multiplied by all of the positive integers FACTORIALS, PERMUTATIONS AND COMBINATIONS
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