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- How many different four-letter words can be formed using the 10 alphabetic letters without repetition, if the word must start with the letter "C" and end with the letter "E", wh
How many different four-letter words can be formed using the 10 alphabetic letters without repetition, if the word must start with the letter "C" and end with the letter "E", while the second and third letters can be any of the remaining three letters?
65
55
66
56
Answers (1)
To calculate the number of different four-letter words that can be formed using the 10 alphabetic letters without repetition, if the word must start with the letter "C" and end with the letter "E", while the second and third letters can be any of the remaining three letters, we can use the concept of permutations.
Since the first and last letters are fixed as "C" and "E" respectively, we have 8 remaining letters to choose from for the second and third positions.
For the second position, we have 8 options. After choosing the second letter, we have 7 options remaining for the third position. Finally, the last position is fixed as "E".
The total number of different four-letter words that satisfy the given conditions can be calculated as:
1 (fixed "C") 8 (options for the second position)
7 (options for the third position)
1 (fixed "E") = 56
Therefore, there are 56 different four-letter words that can be formed using the 10 alphabetic letters without repetition, where the word must start with "C" and end with "E", while the second and third letters can be any of the remaining three letters.
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