There are 6 different letters in the word MONDAY. Show
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(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 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, UPLOAD PHOTO AND GET THE ANSWER NOW! 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. How many words of 4 letters with or without meaning are made from the letters of the word English?So, the total arrangement is given by, 10×9×8×7=5040 . Therefore, the number of words that can be formed is 5040. How many words with or without meaning can be made from the letters of the word Tuesday assuming that no letter is repeated if?Thus total number of permutations= 2×120=240. How many words with or without meaning can be made from the letters of the word Covid?Detailed Solution The correct answer is 120. No of letters in COVID= 5. Now as one letter had already taken place, the number of letters left to be filled at tens place is 4. The number of letters left to be filled at a hundred's place is 3. How many 4Therefore, the number of ways in which four letters of the word MATHEMATICS can be arranged is 2454. How many words of 4 letters with or without meaning are made from the letters of the word English?So, the total arrangement is given by, 10×9×8×7=5040 . Therefore, the number of words that can be formed is 5040.
How many 4(i) Number of 4-letter words that can be formed from the letters of the word MONDAY without repetition of letters is 360.
How many 3 letter words with or without meaning can be formed out of the letters of the word MONDAY when repetition of words is allowed?Therefore, the number of words that can be formed using all the letters of the word MONDAY, using each letter exactly once is 6×5×4×3×2×1=6! =720.
How many words with or without meaning can be made from the letters of the word Sunday assuming that no letter is repeated?Thus total number of permutations= 2×120=240.
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