How many 2​-letter code words can be formed from the letters Upper B comma Upper C comma Upper A comma Upper O comma Upper Q comma Upper W if no letter is​ repeated? If letters can be​ repeated? If adjacent letters must be​ different?

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Answer:

no letter is repeated: 30 words

letters can be repeated: 36 words

adjacent letters different: 30 words

Step-by-step explanation:

We have a total of 6 letters to create a 2-letter code, so if the letters can't be repeated, the first letter has 6 possible values and the second letter has 5 possible values, so the number of 2-letter code words is:

N = 6*5 = 30 words

If the letters can be repeated, each letter has 6 possible values, then we have:

N = 6*6 = 36 words

If adjacent letters must be different, the two letters in the code must be different, because they are adjacent to each other, so we have:

N = 6*5 = 30 words