To solve this problem, we need to use the concept of permutations in combinatorics.

Step 1: Identify the number of letters in the word 'EDUCATION'. There are 9 letters in total.

Step 2: Since the word always starts with the letter 'D', we have already used one letter. So, we are left with 8 letters.

Step 3: Identify if there are any repeating letters. In this case, there are no repeating letters.

Step 4: The number of ways to arrange 'n' distinct items is given by the formula n!. So, the number of ways to arrange the remaining 8 letters is 8!.

Step 5: Therefore, the number of different words that can be formed using the letters of the word 'EDUCATION' such that the word always starts with the letter 'D' is 8! = 40,320.

Question

To solve this problem, we need to use the concept of permutations in combinatorics.

Step 1: Identify the number of letters in the word 'EDUCATION'. There are 9 letters in total.

Step 2: Since the word always starts with the letter 'D', we have already used one letter. So, we are left with 8 letters.

Step 3: Identify if there are any repeating letters. In this case, there are no repeating letters.

Step 4: The number of ways to arrange 'n' distinct items is given by the formula n!. So, the number of ways to arrange the remaining 8 letters is 8!.

Step 5: Therefore, the number of different words that can be formed using the letters of the word 'EDUCATION' such that the word always starts with the letter 'D' is 8! = 40,320.

Knowee AI · Accepted Answer

To solve this problem, we need to use the concept of permutations in combinatorics.

Step 1: Identify the number of letters in the word 'EDUCATION'. There are 9 letters in total.

Step 2: Since the word always starts with the letter 'D', we have already used one letter. So, we are left with 8 letters.

Step 3: Identify if there are any repeating letters. In this case, there are no repeating letters.

Step 4: The number of ways to arrange 'n' distinct items is given by the formula n!. So, the number of ways to arrange the remaining 8 letters is 8!.

Step 5: Therefore, the number of different words that can be formed using the letters of the word 'EDUCATION' such that the word always starts with the letter 'D' is 8! = 40,320.

How many different words can be formed using the letters of the word ‘EDUCATION‘ such that, the word always starts with the letter “D" ?

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