Essential Question: How do you determine the number of distinguishable permutations in the letters of a word? Demonstrated in writing in practice problems. ο Permutation- an ordering of n objects ο Factorial- represented by ! ο π! = 1 β 2 β 3 β 4 β 5 β β― β (π β 1) β π ο 5! = 1 β 2 β 3 β 4 β 5 = 120 ο 7! = 1 β 2 β 3 β 4 β 5 β 6 β 7 = 5040 EQ: How do you determine the number of distinguishable permutations in the letters of a word? Demonstrated in writing in practice problems. ο Two Events If one event can occur in m ways and another event can occur in n ways, then the number of ways that both events can occur is m β n. ο Three or More Events The fundamental counting principle can be extended to three or more events. For example, if three events occur in m, n, and p ways, then the number of ways that all three events can occur is m β n β p. EQ: How do you determine the number of distinguishable permutations in the letters of a word? Demonstrated in writing in practice problems. EQ: How do you determine the number of distinguishable permutations in the letters of a word? Demonstrated in writing in practice problems. EQ: How do you determine the number of distinguishable permutations in the letters of a word? Demonstrated in writing in practice problems. EQ: How do you determine the number of distinguishable permutations in the letters of a word? Demonstrated in writing in practice problems. ο In how many different ways can the baseball teams finish the competition? ο In how many different ways can 3 of the baseball teams finish first, second, and third? EQ: How do you determine the number of distinguishable permutations in the letters of a word? Demonstrated in writing in practice problems. ο The number of permutations of r objects taken from a group of n distinct objects is denoted by nPr ο π π·π = π! πβπ ! ο For permutations order matters ο ABC is not the same as ACB or BAC EQ: How do you determine the number of distinguishable permutations in the letters of a word? Demonstrated in writing in practice problems. EQ: How do you determine the number of distinguishable permutations in the letters of a word? Demonstrated in writing in practice problems. 2) How many different 7 digit telephone numbers are possible if all of the digits can be repeated? 3) In example 3, how many different ways can the teams finish if there are 6 teams competing in the playoffs? 4) You were left a list of 9 chores to complete. In how many orders can you complete 5 of the chores? EQ: How do you determine the number of distinguishable permutations in the letters of a word? Demonstrated in writing in practice problems. ο The number of distinguishable permutations of n objects where one object is repeated s1 times, another is repeated s2 times, and so on, is: π! π 1 ! β π 2 ! β π 3 ! β β― β π π ! EQ: How do you determine the number of distinguishable permutations in the letters of a word? Demonstrated in writing in practice problems. EQ: How do you determine the number of distinguishable permutations in the letters of a word? Demonstrated in writing in practice problems. ο TOMORROW ο YESTERDAY EQ: How do you determine the number of distinguishable permutations in the letters of a word? Demonstrated in writing in practice problems.
© Copyright 2026 Paperzz