1). don 2). mod 3). mon 4). and 5). any 6). nam 7). nay 8). nod 9). nom 10). yam 11). moa 12). dom 13). yon 14). yod 15). mad 16). ado 17). man 18). day 19). may 20). dam Show
2 letter Words made out of monday1). oy 2). om 3). yo 4). od 5). on 6). am 7). ad 8). do 9). ma 10). mo 11). ay 12). my 13). an 14). na 15). no 16). ya (i) Number of 4-letter words that can be formed from the letters of the word MONDAY, without repetition of letters, is the number of permutations of 6 different objects taken 4 at a time, which is `""^6P_4`. Thus, required number of words that can be formed using 4 letters at a time is  (ii) Number of words that can be formed by using all the letters of the word MONDAY at a time is the number of permutations of 6 different objects taken 6 at a time, which is `""^6P_6 = 6!`. Thus, required number of words that can be formed when all letters are used at a time = 6! = 6 × 5 × 4 × 3 × 2 ×1 = 720 (iii) In the given word, there are 2 different vowels, which have to occupy the rightmost place of the words formed. This can be done only in 2 ways. Since the letters cannot be repeated and the rightmost place is already occupied with a letter (which is a vowel), the remaining five places are to be filled by the remaining 5 letters. This can be done in 5! ways. (i) Number of 4-letter words that can be formed from the letters of the word MONDAY, without repetition of letters, is the number of permutations of 6 different objects taken 4 at a time, which is `""^6P_4`. Thus, required number of words that can be formed using 4 letters at a time is (ii) Number of words that can be formed by using all the letters of the word MONDAY at a time is the number of permutations of 6 different objects taken 6 at a time, which is `""^6P_6 = 6!`. Thus, required number of words that can be formed when all letters are used at a time = 6! = 6 × 5 × 4 × 3 × 2 ×1 = 720 (iii) In the given word, there are 2 different vowels, which have to occupy the rightmost place of the words formed. This can be done only in 2 ways. Since the letters cannot be repeated and the rightmost place is already occupied with a letter (which is a vowel), the remaining five places are to be filled by the remaining 5 letters. This can be done in 5! ways. Thus, in this case, required number of words that can be formed is 5! × 2 = 120 × 2 = 240 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 the first letter is a vowel?Answer Verified Hint: Here we go through by applying the properties of permutation and combination for arranging the letters to form the word. As we know if we select r out of n it can be written as ${}^n{C_r}$ and if we permute r out of n it can be written as ${}^n{P_r}$. Complete step-by-step answer: (i) Number of 4-letter words that can be formed from the letters of the word MONDAY, without repetition of letters, is the number of permutations of 6 different objects taken 4 at a time, which is ${}^6{P_4}$. (ii) There are 6 different letters in the word MONDAY. (iii) Total number of letters in the word MONDAY is 6, Number of vowels are 2 i.e. (O, A) Note: Whenever we face such type of question the key concept for solving the question is go through the properties of permutation and combination as we know if there are n places and n numbers are given then first place can filled by n choice then second place can be fill by (n-1) choice and so on. This property is the golden rule for solving such types of questions. Home > English > Class 11 > Maths > Chapter > Permutations And Combinations > How many words, with or witho... Get Answer to any question, just click a photo and upload the photo and get the answer completely free, How many different arrangements can be made with the letters of the word MONDAY?∴ Number of ways = 1×4×4×3×2×1=96.
How many different arrangements of the letters in the word MONDAY can be formed if the vowels must be kept next to each other?=120. Since we have to keep vowels separate then we will first find the number of ways in which vowels can be together and subtract it from total.
How many words can be formed from the word MONDAY with the two vowel always occurring together?Therefore, total number of ways = 120×2C1=120×2=240 ways.
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