Question
Download Solution PDFHow many words, no matter if they are meaningless, can be formed by the letters of the word 'DIARY'?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe correct answer is None of the above.
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
- 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
Last updated on Jul 4, 2025
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