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How many 4-letter words with or without meaning, can be formed out of the letters of the word, ‘LOGARITHMS’, if repetition of letters is not allowed?
- a)40
- b)400
- c)5040
- d)2520
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
How many 4-letter words with or without meaning, can be formed out of ...
'LOGARITHMS' contains 10 different letters.
Required number of words = Number of arrangements of 10 letters, taking 4 at a time.
= 10P4
= 5040.
Most Upvoted Answer
How many 4-letter words with or without meaning, can be formed out of ...
Approach:
To find the number of 4-letter words that can be formed from the letters of the word 'LOGARITHMS' without repetition, we can use the concept of permutations.
Calculation:
- 'LOGARITHMS' has 10 letters.
- Number of ways to choose 4 letters out of 10 without repetition = 10P4 = 10! / (10-4)!
- Number of ways to arrange 4 selected letters = 4!
Total number of 4-letter words:
Total number of 4-letter words = 10P4 * 4!
Solving:
10P4 = 10! / 6! = 10 * 9 * 8 * 7
4! = 4 * 3 * 2 * 1
Total number of 4-letter words = 10 * 9 * 8 * 7 * 4 * 3 * 2 * 1 = 5040
Therefore, the number of 4-letter words that can be formed from the letters of the word 'LOGARITHMS' without repetition is 5040. Hence, the correct answer is option C.
To find the number of 4-letter words that can be formed from the letters of the word 'LOGARITHMS' without repetition, we can use the concept of permutations.
Calculation:
- 'LOGARITHMS' has 10 letters.
- Number of ways to choose 4 letters out of 10 without repetition = 10P4 = 10! / (10-4)!
- Number of ways to arrange 4 selected letters = 4!
Total number of 4-letter words:
Total number of 4-letter words = 10P4 * 4!
Solving:
10P4 = 10! / 6! = 10 * 9 * 8 * 7
4! = 4 * 3 * 2 * 1
Total number of 4-letter words = 10 * 9 * 8 * 7 * 4 * 3 * 2 * 1 = 5040
Therefore, the number of 4-letter words that can be formed from the letters of the word 'LOGARITHMS' without repetition is 5040. Hence, the correct answer is option C.
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How many 4-letter words with or without meaning, can be formed out of the letters of the word, ‘LOGARITHMS’, if repetition of letters is not allowed?a)40b)400c)5040d)2520Correct answer is option 'C'. Can you explain this answer?
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