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← How many 2-letter code words can be formed from the letters Y, E, T, A, J if no letter is repeated? If letters can be repeated? If adjacent letters must be different? There are possible 2-letter code words if no letter is repeated. (Type a whole number) There are possible 2-letter code words if letters can be repeated. (Type a whole number.) There are possible 2-letter code words if adjacent letters must be different. (Type a whole number)​

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Answer:

Explanation:

If no letter is repeated, there are 20 possible 2-letter code words that can be formed.

To find the number of possible code words, you use the formula for permutations:

nPr = n! / (n - r)!

where n is the number of letters available and r is the number of letters you want to choose.

In this case, n = 5 (since there are 5 letters available) and r = 2 (since we want to choose 2 letters). So, we get:

nPr = 5! / (5 - 2)! = 5! / 3! = 5 x 4 = 20

If letters can be repeated, there are 25 possible 2-letter code words that can be formed.

To find the number of possible code words, you use the formula for combinations:

nCr = (n + r - 1)! / r!(n - 1)!

where n is the number of letters available and r is the number of letters you want to choose.

In this case, n = 5 (since there are 5 letters available) and r = 2 (since we want to choose 2 letters). So, we get:

nCr = (5 + 2 - 1)! / 2!(5 - 1)! = 6! / 2!4! = 15

If adjacent letters must be different, there are 60 possible 2-letter code words that can be formed.

To find the number of possible code words, you first choose one letter from the available 5 letters. Then, you choose one letter from the remaining 4 letters (since it must be different from the first letter). So, we get:

5 x 4 = 20

However, since order matters (e.g. TE and ET are different), you multiply by 2 to get:

20 x 2 = 40

So, there are 40 possible 2-letter code words if adjacent letters must be different.

User Abhijith Nagaraja
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