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?

Asked by Pragya Singh | 1 year ago | 70

**(i)** Number of 4-letter words that can be formed from the letters of the given word without repetition is permutations of 6 different objects taken 4 at a time.

Therefore, Number of 4 letter words that can be formed

\( ^6P_4=\dfrac{6!}{(6-4)}=\dfrac{6!}{2!}\)

= \( 6\times 5\times 4\times 3\)

= 360

**(ii)** Words that can be formed using all the letters of the given word is permutation of 6 different objects taken 6 at a time

\( ^6P_6=6!\)

Therefore, number of words that can be formed is

= \(6!= 6\times 5\times 4\times 3\times 2\times 1=720\)

**(iii) **There are two different vowels in the word MONDAY which occupies the rightmost place of the words formed. Hence, there are 2 ways. Since, it is without repetition and the rightmost place is occupied, the remaining five vacant places can be filled by 5 different letters. Hence, 5! Ways. Therefore, number of words that can be formed = \( 5!\times 2=120\times 2=240\)

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**(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 ?

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