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In how many ways can the letters of the word CALCULATOR be rearranged?
- a)4,53,599
- b)4,53,600
- c)4,54,800
- d)4,53,900
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
In how many ways can the letters of the word CALCULATOR be rearranged?...
Total letters = 10
C comes two times.
A comes two times.
L comes two times.
So the answer = 4,53,600 – 1 = 4,53,599
C comes two times.
A comes two times.
L comes two times.
So the answer = 4,53,600 – 1 = 4,53,599
Most Upvoted Answer
In how many ways can the letters of the word CALCULATOR be rearranged?...
Understanding the Problem
To find the number of ways to rearrange the letters of the word "CALCULATOR," we need to account for the repetitions of letters.
Identifying the Letters and Their Frequencies
- The word "CALCULATOR" has 10 letters.
- The frequency of each letter is:
- C: 2
- A: 2
- L: 2
- U: 1
- T: 1
- O: 1
- R: 1
Applying the Formula for Permutations of Multisets
The formula for the number of arrangements of letters when some letters are repeated is:
Total arrangements = (Total letters)! / (Product of the factorial of each letter's frequency)
For "CALCULATOR":
- Total letters = 10
- Factorials of frequencies:
- C: 2!
- A: 2!
- L: 2!
- U: 1!
- T: 1!
- O: 1!
- R: 1!
The calculation is as follows:
Total arrangements = 10! / (2! * 2! * 2! * 1! * 1! * 1! * 1!)
Calculating the Factorials
- 10! = 3,628,800
- 2! = 2, so 2! * 2! * 2! = 2 * 2 * 2 = 8
- 1! = 1, so it contributes nothing additional.
Now, substituting the values:
Total arrangements = 3,628,800 / 8 = 453,600
Final Answer
Thus, the total number of ways to rearrange the letters of the word "CALCULATOR" is 453,600.
The correct answer is option B) 453,600.
To find the number of ways to rearrange the letters of the word "CALCULATOR," we need to account for the repetitions of letters.
Identifying the Letters and Their Frequencies
- The word "CALCULATOR" has 10 letters.
- The frequency of each letter is:
- C: 2
- A: 2
- L: 2
- U: 1
- T: 1
- O: 1
- R: 1
Applying the Formula for Permutations of Multisets
The formula for the number of arrangements of letters when some letters are repeated is:
Total arrangements = (Total letters)! / (Product of the factorial of each letter's frequency)
For "CALCULATOR":
- Total letters = 10
- Factorials of frequencies:
- C: 2!
- A: 2!
- L: 2!
- U: 1!
- T: 1!
- O: 1!
- R: 1!
The calculation is as follows:
Total arrangements = 10! / (2! * 2! * 2! * 1! * 1! * 1! * 1!)
Calculating the Factorials
- 10! = 3,628,800
- 2! = 2, so 2! * 2! * 2! = 2 * 2 * 2 = 8
- 1! = 1, so it contributes nothing additional.
Now, substituting the values:
Total arrangements = 3,628,800 / 8 = 453,600
Final Answer
Thus, the total number of ways to rearrange the letters of the word "CALCULATOR" is 453,600.
The correct answer is option B) 453,600.
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Community Answer
In how many ways can the letters of the word CALCULATOR be rearranged?...
Total letters = 10
C comes two times.
A comes two times.
L comes two times.
So the answer = 4,53,600 – 1 = 4,53,599
C comes two times.
A comes two times.
L comes two times.
So the answer = 4,53,600 – 1 = 4,53,599
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Question Description
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