9/8/2023 0 Comments Permutation order mattersPresident last, and there would've only been Vice President, and there would've still beenĮight choices. The nine people, there's the 9 for President times the 8įor Vice President times the 7 for Secretary. So if you want to think aboutĪll of the different ways there are to choose a board from Left for Secretary? Well, now there's only seven To be Vice President? Well, now there's onlyĮight possible candidates for Vice President? Eight possibilities. One of the nine is going to be President. President, so one of the nine is going to be President. Out of the running for the other two offices. So there's nine possibilities for President. There for President? Well, the club has nine people, President slot first and we haven't appointed any Have the Vice President, VP, and then you have President, then I'm no longer a valid person for Vice One person can't hold more than one office. To choose the board from the nine people? Now, we're going to assume that To choose a board of three officers: a President, a Vice "TITTER"), then we'd divide by 3!, because there are 3! ways to arrange T1, T2, and T3. The general idea is that once we count the number of ways to arrange all letters (treated as being distinct), we need to divide by the number of ways to arrange the repeated letters. Hence, 5!/2 is the number of unique ways to arrange the letters of HAPPY. So when we compute 5!, so know that we need to divide that number by 2 to account for switching the P's about. Therefore, for every single arrangement of the 5 letters, we can make another identical one by switching the P's. When we start with 5!, we are over-counting: the factorial doesn't realize that the two P's are identical, it treats all 5 letters as distinct. One arrangement of the letters is, of course: H A P1 P2 Yīut in practice, since P1 and P2 cannot be distinguished, these two are equivalent arrangements of the letters. Using the word "HAPPY" (let's distinguish the P's as P1 and P2). There is no need to relate to previous videos, you state all the information needed to answer your question.
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