How many 2-letter "words" consist of two different letters arranged in alphabetical order? (Any two letters together is considered a "word." For example, one such word is dq.)
Number of possible 2 letter arrangements = 26x25 = 650
BUT, half of those would be in the wrong alphabetical order, e.g.
they would contain rt and tr, one is right the other wrong, so..
number of ways for your problem = 650/2 = 325
To find the number of 2-letter "words" consisting of two different letters arranged in alphabetical order, we can follow these steps:
Step 1: Determine the number of choices for the first letter.
The first letter can be any of the 26 letters of the English alphabet. Since there are no restrictions on the first letter, we have 26 choices.
Step 2: Determine the number of choices for the second letter.
The second letter must be different from the first letter and come after it in alphabetical order. If the first letter is 'a', the second letter can be any of the remaining 25 letters ('b' through 'z'). If the first letter is 'b', the second letter can be any of the remaining 24 letters ('c' through 'z'), and so on.
Step 3: Calculate the total number of "words".
To find the total number of "words," we need to multiply the number of choices in Step 1 by the number of choices in Step 2.
In this case, the number of choices for the first letter is fixed at 26 since it can be any of the 26 letters.
For the second letter, since the alphabetical order is required, the choices depend on the first letter as follows:
- If the first letter is 'a', we have 25 choices for the second letter.
- If the first letter is 'b', we have 24 choices for the second letter.
- If the first letter is 'c', we have 23 choices for the second letter.
- And so on, until the first letter 'y' is reached, which leaves only 1 choice for the second letter ('z').
To calculate the total number of "words," we need to sum up the number of choices for the second letter across all possible first letters.
Thus, the total number of 2-letter "words" consisting of two different letters arranged in alphabetical order is:
2-letter words = 25 + 24 + 23 + ... + 1
= (25 * 26) / 2
= 325
Therefore, there are a total of 325 2-letter "words" consisting of two different letters arranged in alphabetical order.