Assistance on math word problem

(Question)

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. John 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 answer are correct, and which are not, and why? Explain your answers clearly and thoroughly, drawing on the meaning of multiplication.

Re: Assistance on math word problem

This is a 'multiplication principle' problem. If you have 3 events in order, say E1 E2 E3... And E1 has N1 ways of doing it, E2 has N2 ways of doing it and E3 has N3 ways of doing it, then there are N1 * N2 * N3 ways of doing E1 then E2 then E3.

So, look that up in your textbook. In this case there are 26 * 25 possible ways to pick a 2 letter sequence without repeating letters. Hope that is helpful.