![]() Substitute the values for □ and □ to get that the Since the number of permutations of □ objectsĬhosen from a group of □ objects is equal to □ □ − □, we can Īlternatively, we could observe that each student ID is a permutation of 7 digits chosenįrom a group of 10 digits. ![]() This way is obtained by finding the product of the number of choices for each digit, which The total number of ways of choosing a 7-digit ID in There are 10 choices for the 1st digit, and each time we use a digit we cannot use itĪgain, so the number of choices for each subsequent digit is reduced by 1 until there are Order of the objects matters, so we have to count permutations. Permutations or combinations of a set of objects. Counting the number of outcomes often requires finding the number of ![]() Recall that when calculating the probability of an event, we need to calculate the total Counting orderings of this type involves counting combinations, which we do not Would be the same as the outcome BA because both outcomes result in Anna and Billy becoming However, if we instead wanted to choose two vice-captains, then the outcome AB In the firstĮxample, the outcome AB (Anna for captain and Billy for vice-captain) is different from the This is because the order in which we selected the items mattered. In both of the above examples, we found that each outcome could be described by a The number of ways to choose an ordered arrangement of □ objects from a Counting the Number of Ordered Arrangements of □ Items Chosen from a Group of □
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