Question: Suppose that we want to write down a string of three letters in alphabetical order, where we can repeat letters. So AAA. EEL. and

Suppose that we want to write down a string of three letters 

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 26 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?

Step by Step Solution

3.39 Rating (158 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!