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?
(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 = \( 5!\times 2=120\times 2=240\)
Answered by Abhisek | 1 year agoHow many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?
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How many words, with or without meaning can be formed 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 ?
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How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?