Question

If John, Trey, and Miles want to know how’ | many two-letter secret codes there are that don't have a repeated letter. For example, they want to : cou

Probability and combinatorics
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asked 2021-05-05
If John, Trey, and Miles want to know how’ | many two-letter secret codes there are that don't have a repeated letter. For example, they want to : count BA and AB, but they don't want to count“ doubles such as ZZ or XX. Jobn says there are 26 + 25 because you don’t want to use the same letter twice; that’s why the second number is 25.
‘Trey says he thinks it should be times, not plus: 26-25, Miles says the number is 26-26 ~ 26 because you need to take away the double letters. Discuss the boys’ ideas, Which answers are correct, which are not, and why? Explain your answers clearly and thoroughly, drawing ‘on this section’s definition of multiptication.. -

Expert Answers (1)

2021-05-06
Trey and Miles are correct — we can either use the reasoning “we do not want for the two letters to be the same, so for the first letter we have 26 choices and for the second we have 25”, so we get 26-25, or we can find the number of all two-letter codes, which we have 26-26, and subtract the number of two-letter codes with a repeated letter, which we have 26.
Adding 26 and 25 makes no sense, since for each choice of the first letter we have 2% additional codes.
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