Suppose that we want to write down a string of three letters in alphabetical order, where...

 

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Suppose that we want to write down a string of three letters in alphabetical order, where we can repeat letters. So AAA. EEL. and XYZ are all valid, but CAT, ZYX and ELE are not. Suppose that someone tells you the following: "The correct number of strings is 26/3!. This is because if order mattered we could pick 26 options for each letter, so there would be 26 possibilities. But since order doesn't matter there will always be six answers that correspond to the same result, since we can reorder three items in 3!= 6 ways. For example, XYZ would correspond to XYZ. XZY, YXZ, YZX, ZXY and ZYX. So we need to divide 26³ by 6 to get the correct answer. This explanation is wrong. Explain why 26/3! is not the correct answer • What is the correct number of possible strings? Suppose that we want to write down a string of three letters in alphabetical order, where we can repeat letters. So AAA. EEL. and XYZ are all valid, but CAT, ZYX and ELE are not. Suppose that someone tells you the following: "The correct number of strings is 26/3!. This is because if order mattered we could pick 26 options for each letter, so there would be 26 possibilities. But since order doesn't matter there will always be six answers that correspond to the same result, since we can reorder three items in 3!= 6 ways. For example, XYZ would correspond to XYZ. XZY, YXZ, YZX, ZXY and ZYX. So we need to divide 26³ by 6 to get the correct answer. This explanation is wrong. Explain why 26/3! is not the correct answer • What is the correct number of possible strings?