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How many words, no matter if they are meaningless, can be formed by the letters of the word 'DIARY'?
- a)24
- b)5
- c)10
- d)None of these
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
How many words, no matter if they are meaningless, can be formed by th...
Explanation:
To find the number of words that can be formed using the letters of the word "DIARY", we need to consider the number of permutations that can be made using these letters.
The word "DIARY" has 5 letters.
To calculate the number of permutations, we use the formula:
n! / (n1! * n2! * n3! * ...)
Where n is the total number of letters and n1, n2, n3, ... are the number of occurrences of each repeated letter.
In the word "DIARY", there are no repeated letters. Therefore, the formula simplifies to:
5! / (1! * 1! * 1! * 1! * 1!)
= 5! / 1
= 5 * 4 * 3 * 2 * 1 / 1
= 120
So, there are a total of 120 permutations or words that can be formed using the letters of the word "DIARY".
However, the question specifically asks for the number of words, irrespective of their meaning.
Meaningful words that can be formed using the letters of the word "DIARY" are: "DIARY", "YARD", "AIRY", "DRY", "RAD", "AID", "DAY", "RAY", "RID", "YID", "DAR", "RYA", "RIA", "ARD", "YAR", "AD", "AI", "ID", "AR", "AY", "YI", "YA", "RAD", "RID", "DRY", "AIR", "YARD", "RAID", "RAY", "DAY", "DIR", "RADI", "RYAD", "YARDI", "RAIDY", "RADYI", "IYARD", "AIYRD", "IYDAR", "IYRDA", "YIARD", "YIADR", "ARID", "DARYI", "DAR
To find the number of words that can be formed using the letters of the word "DIARY", we need to consider the number of permutations that can be made using these letters.
The word "DIARY" has 5 letters.
To calculate the number of permutations, we use the formula:
n! / (n1! * n2! * n3! * ...)
Where n is the total number of letters and n1, n2, n3, ... are the number of occurrences of each repeated letter.
In the word "DIARY", there are no repeated letters. Therefore, the formula simplifies to:
5! / (1! * 1! * 1! * 1! * 1!)
= 5! / 1
= 5 * 4 * 3 * 2 * 1 / 1
= 120
So, there are a total of 120 permutations or words that can be formed using the letters of the word "DIARY".
However, the question specifically asks for the number of words, irrespective of their meaning.
Meaningful words that can be formed using the letters of the word "DIARY" are: "DIARY", "YARD", "AIRY", "DRY", "RAD", "AID", "DAY", "RAY", "RID", "YID", "DAR", "RYA", "RIA", "ARD", "YAR", "AD", "AI", "ID", "AR", "AY", "YI", "YA", "RAD", "RID", "DRY", "AIR", "YARD", "RAID", "RAY", "DAY", "DIR", "RADI", "RYAD", "YARDI", "RAIDY", "RADYI", "IYARD", "AIYRD", "IYDAR", "IYRDA", "YIARD", "YIADR", "ARID", "DARYI", "DAR
Community Answer
How many words, no matter if they are meaningless, can be formed by th...
The correct answer is None of the above.
Key Points
Key Points
Total number of letters = 5
Number of repeating letters = 0
The total number of words that can be formed are = 5P5
= 5!
= 120
∴The total number of words that can be formed is 120.
Alternate Method
Alternate Method
- There are 5 different letters in the word DIARY.
- The first place can be filled in 5 ways.
- The second place can be filled by any one of the remaining 4 letters. So, second place can be filled in 4 ways.
- So, on continuing, the number of ways of filling third place in 3 ways, fourth place in 2 ways, fifth place in 1 way.
- Therefore, the number of words that can be formed using all the letters of the word DIARY, using each letter exactly once is 5×4×3×2×1 = 5! = 120
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How many words, no matter if they are meaningless, can be formed by the lettersof the word DIARY?a)24b)5c)10d)None of theseCorrect answer is option 'D'. Can you explain this answer?
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