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

##### Solution :-

(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 ago

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