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The number of ways in which the letters of the word DOGMATIC can be arranged is
- a)40319
- b)40320
- c)40321
- d)none of these
Correct answer is 'A'. Can you explain this answer?
Verified Answer
The number of ways in which the letters of the word DOGMATIC can be ar...
Answer is b) 40320
All letters in the word are distinct.
So, 8 letters can be permuted in 8! = 40,320 ways.
Most Upvoted Answer
The number of ways in which the letters of the word DOGMATIC can be ar...
Given word: DOGMATIC
To find: Number of ways in which the letters can be arranged
Approach:
1. Find the total number of letters in the given word.
2. As there are repeating letters in the word, we need to find the number of permutations of the repeating letters and divide the total number of permutations by that factor to avoid overcounting.
3. Use the formula n!/(n1!n2!...nk!), where n is the total number of letters, and n1, n2, ..., nk are the number of repeating letters.
Calculation:
1. Total number of letters in the word = 7
2. Number of repeating letters:
- 2 times letter D
- 1 time letter O
- 1 time letter G
- 1 time letter M
- 1 time letter A
- 1 time letter T
3. Number of permutations of repeating letters:
- D: 2! = 2
- O: 1! = 1
- G: 1! = 1
- M: 1! = 1
- A: 1! = 1
- T: 1! = 1
4. Total number of permutations = 7!/(2!1!1!1!1!1!) = 5040/2 = 2520
Answer: The number of ways in which the letters of the word DOGMATIC can be arranged is 40320.
To find: Number of ways in which the letters can be arranged
Approach:
1. Find the total number of letters in the given word.
2. As there are repeating letters in the word, we need to find the number of permutations of the repeating letters and divide the total number of permutations by that factor to avoid overcounting.
3. Use the formula n!/(n1!n2!...nk!), where n is the total number of letters, and n1, n2, ..., nk are the number of repeating letters.
Calculation:
1. Total number of letters in the word = 7
2. Number of repeating letters:
- 2 times letter D
- 1 time letter O
- 1 time letter G
- 1 time letter M
- 1 time letter A
- 1 time letter T
3. Number of permutations of repeating letters:
- D: 2! = 2
- O: 1! = 1
- G: 1! = 1
- M: 1! = 1
- A: 1! = 1
- T: 1! = 1
4. Total number of permutations = 7!/(2!1!1!1!1!1!) = 5040/2 = 2520
Answer: The number of ways in which the letters of the word DOGMATIC can be arranged is 40320.
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Community Answer
The number of ways in which the letters of the word DOGMATIC can be ar...
We are asked to find the number of ways in which the letters of the word "DOGMATIC" can be arranged.
Step 1: Count the Total Number of Letters
The word "DOGMATIC" has 8 letters in total:
The word "DOGMATIC" has 8 letters in total:
D, O, G, M, A, T, I, C
Step 2: Check for Repetition of Letters
In this case, all the letters in "DOGMATIC" are distinct, meaning no letters are repeated.
In this case, all the letters in "DOGMATIC" are distinct, meaning no letters are repeated.
Step 3: Calculate the Total Number of Arrangements
Since all the letters are distinct, the total number of ways to arrange 8 distinct letters is given by the factorial of the number of letters:
Since all the letters are distinct, the total number of ways to arrange 8 distinct letters is given by the factorial of the number of letters:
8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40320
Final Answer:
The number of ways in which the letters of the word "DOGMATIC" can be arranged is 40320.
The number of ways in which the letters of the word "DOGMATIC" can be arranged is 40320.
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