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How many different words can be formed with the letters of the word ‘BHARAT’?
In how many of these B and H are never together?
- a)240, 180
- b)360, 240
- c)320, 200
- d)380, 260
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
How many different words can be formed with the letters of the word ‘...
To find the number of different words that can be formed with the letters of the word ‘BHARAT’, we can use the concept of permutations.
The word ‘BHARAT’ consists of 6 letters.
Number of letters = 6
Number of distinct letters = 5 (B, H, A, R, T)
Number of repetitions of each letter = 1,1,2,1,1 (B: 1, H: 1, A: 2, R: 1, T: 1)
To find the number of different words, we can use the formula for permutations with repetitions.
The formula is given by:
Number of different words = (total number of letters)! / (repetitions of each letter)!
Let's calculate the number of different words:
Number of different words = 6! / (1! * 1! * 2! * 1! * 1!)
= (6 * 5 * 4 * 3 * 2 * 1) / (1 * 1 * 2 * 1 * 1)
= 720 / 2
= 360
Therefore, there are 360 different words that can be formed with the letters of the word ‘BHARAT’.
Next, let's find the number of words in which B and H are never together. We can use the concept of permutations with restrictions to solve this problem.
To find the number of words in which B and H are never together, we can consider B and H as a single letter. Let's call this new letter X.
Now, we have 5 letters: X, A, R, A, T.
Number of letters = 5
Number of distinct letters = 4 (X, A, R, T)
Number of repetitions of each letter = 1, 2, 1, 1 (X: 1, A: 2, R: 1, T: 1)
Using the formula for permutations with repetitions, we can calculate the number of different words:
Number of different words = 5! / (1! * 2! * 1! * 1!)
= (5 * 4 * 3 * 2 * 1) / (1 * 2 * 1 * 1)
= 120 / 2
= 60
Therefore, there are 60 different words in which B and H are never together.
Hence, the correct answer is option B: 360, 240.
The word ‘BHARAT’ consists of 6 letters.
Number of letters = 6
Number of distinct letters = 5 (B, H, A, R, T)
Number of repetitions of each letter = 1,1,2,1,1 (B: 1, H: 1, A: 2, R: 1, T: 1)
To find the number of different words, we can use the formula for permutations with repetitions.
The formula is given by:
Number of different words = (total number of letters)! / (repetitions of each letter)!
Let's calculate the number of different words:
Number of different words = 6! / (1! * 1! * 2! * 1! * 1!)
= (6 * 5 * 4 * 3 * 2 * 1) / (1 * 1 * 2 * 1 * 1)
= 720 / 2
= 360
Therefore, there are 360 different words that can be formed with the letters of the word ‘BHARAT’.
Next, let's find the number of words in which B and H are never together. We can use the concept of permutations with restrictions to solve this problem.
To find the number of words in which B and H are never together, we can consider B and H as a single letter. Let's call this new letter X.
Now, we have 5 letters: X, A, R, A, T.
Number of letters = 5
Number of distinct letters = 4 (X, A, R, T)
Number of repetitions of each letter = 1, 2, 1, 1 (X: 1, A: 2, R: 1, T: 1)
Using the formula for permutations with repetitions, we can calculate the number of different words:
Number of different words = 5! / (1! * 2! * 1! * 1!)
= (5 * 4 * 3 * 2 * 1) / (1 * 2 * 1 * 1)
= 120 / 2
= 60
Therefore, there are 60 different words in which B and H are never together.
Hence, the correct answer is option B: 360, 240.
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Community Answer
How many different words can be formed with the letters of the word ‘...
Out of letters in the word ‘BHARAT' two letters, that is, A's are alike.
∴ Number of permutations = 6!/21 = 360.
Number of words in which B and H are never together = Total number of words - number of words in which B and H are together
= 360 - (5!/2!).2! = 360 - 120 = 240.
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How many different words can be formed with the letters of the word ‘BHARAT’?In how many of these B and H are never together?a)240, 180b)360, 240c)320, 200d)380, 260Correct answer is option 'B'. Can you explain this answer?
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