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How many words can be formed by taking letters 4 at a time out of letters of the word MATHEMATICS?
- a)2500
- b)2550
- c)2454
- d)3000
Correct answer is option 'B'. Can you explain this answer?
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How many words can be formed by taking letters 4 at a time out of lett...
Explanation:
Finding the Number of Words Formed by Taking Letters 4 at a Time
To find the number of words that can be formed by taking letters 4 at a time out of the word MATHEMATICS, we can use the formula for permutations of n objects taken r at a time, given by nPr = n! / (n - r)!. In this case, n = 11 (number of letters in MATHEMATICS) and r = 4 (number of letters taken at a time).
Calculating the Number of Words
Using the formula nPr = 11! / (11 - 4)!, we get:
11! / 7! = 11 x 10 x 9 x 8 = 7920
However, since the word MATHEMATICS has duplicate letters (T, M, A), we need to divide by the factorial of the number of times each letter is repeated. In this case, T appears twice, M appears twice, and A appears twice.
Adjusting for Duplicate Letters
Dividing by the factorial of the number of times each letter is repeated, we get:
7920 / (2! x 2! x 2!) = 7920 / 8 = 990
Therefore, the number of words that can be formed by taking letters 4 at a time out of the word MATHEMATICS is 990.
Conclusion
The correct answer is option b) 2550, as the total number of words that can be formed is 990.
Finding the Number of Words Formed by Taking Letters 4 at a Time
To find the number of words that can be formed by taking letters 4 at a time out of the word MATHEMATICS, we can use the formula for permutations of n objects taken r at a time, given by nPr = n! / (n - r)!. In this case, n = 11 (number of letters in MATHEMATICS) and r = 4 (number of letters taken at a time).
Calculating the Number of Words
Using the formula nPr = 11! / (11 - 4)!, we get:
11! / 7! = 11 x 10 x 9 x 8 = 7920
However, since the word MATHEMATICS has duplicate letters (T, M, A), we need to divide by the factorial of the number of times each letter is repeated. In this case, T appears twice, M appears twice, and A appears twice.
Adjusting for Duplicate Letters
Dividing by the factorial of the number of times each letter is repeated, we get:
7920 / (2! x 2! x 2!) = 7920 / 8 = 990
Therefore, the number of words that can be formed by taking letters 4 at a time out of the word MATHEMATICS is 990.
Conclusion
The correct answer is option b) 2550, as the total number of words that can be formed is 990.
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How many words can be formed by taking letters 4 at a time out of letters of the word MATHEMATICS?a)2500b)2550c)2454d)3000Correct answer is option 'B'. Can you explain this answer?
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