How many words with or without meaning can be formed from all the letters of the word MONDAY assuming that no letter is repeated and first letter is a vowel?
How many words, with or without meaning can be formed from the letters of the word 'MONDAY', assuming that no letter is repeated, if all letters are used but first letter is a vowel? Show
SolutionThere are six letters in the word MONDAY. All the letters are used, but the first letter is a vowel: Concept: Factorial N (N!) Permutations and Combinations Is there an error in this question or solution? APPEARS INHome > English > Class 11 > Maths > Chapter > Permutations And Combinations > How many words, with or withou... 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! 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 can be formed by using all the letters of the word MONDAY if each word start with a consonant?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 formed using all the letters of the word Friday?= 40320. Was this answer helpful?
How many 4So, the total arrangement is given by, 10×9×8×7=5040 .
How many words with or without meaning can be made using the letters of the word Hyderabad?Hence, the number of words are 120. Q.
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