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Question -

How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if.
(i) 4 letters are used at a time,
(ii) All letters are used at a time,
(iii) all letters are used but first letter is a vowel?



Answer -

(i) Number of letters to be used =4
⇒ Number of permutations =
 
(ii) Number of letters to be used = 6
⇒ Number of permutations =
 
(iii) Number of vowels in MONDAY = 2 (O and A)
⇒ Number of permutations in vowel =
 
Now, remaining places = 5
Remaining letters to be used =5
⇒ Number of permutations =
 
Therefore, total number of permutations = 2 × 120 =240.

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