How many different arrangement can be formed from the letters of the word EQUATION?
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Hint: First of all, we have a total of 8 places. Fill the first and the last places by 3 consonants in 3 x 2 ways. Now fill the remaining places with the remaining 6 letters in 6! ways. Remember that there is no constraint in filling places from second to seventh place. Here, we are given a word EQUATION and we have to find the number of words formed by letters of word EQUATION such that the words end and begin with consonants. Note: Here, students get confused if repetition is allowed or not. As it is clearly mentioned that the first and last letters of the word are consonants and words should be formed by letters of the word EQUATION then consider that repetition is not allowed. Also, it would not make sense if repetition is allowed as we can make infinitely many words if the repetition is allowed. Also, some students try to do this question manually by writing different words and counting them one by one which is a very lengthy approach and can give wrong results. Union Public Service Commission (UPSC) has released the NDA Result II 2022 (Name Wise List) for the exam that was held on 4th September 2022. Earlier, the roll number wise list was released by the board. A total number of 400 vacancies will be filled for the UPSC NDA II 2022 exam. The selection process for the exam includes a Written Exam and SSB Interview. Candidates who get successful selection under UPSC NDA II will get a salary range between Rs. 15,600 to Rs. 39,100. Answer VerifiedHint: Permutations are the different ways in which a collection of items can be arranged. For example:The different ways in which the alphabets A, B and C can be grouped together, taken all at a time, are ABC, ACB, BCA, CBA, CAB, BAC. Note that ABC and CBA are not the same as the order of arrangement is different. The same rule applies while solving any problem in Permutations.The number of ways in which n things can be arranged, taken all at a time, \[{}^n{P_n}{\text{ }} = {\text{ }}n!\], called ‘n factorial.’ Complete step-by-step answer: Total number of letters in “EQUATION” = 8.There are 5 vowels: a, e, i, o, u and 3 consonants : q, t, n.Since all the vowels and consonants have to occur together, both (AEIOU) and (QTN) can be assumed as single objects.Then they form 2 groups V(vowels) and C (consonants)We first arrange the 2 groups.The permutations of these 2 objects taken all at a time are counted: ${}^2{P_2} = 2! = 2$waysCorresponding to each of these permutations, Now the group V has 5 elements, they can be arranged in $5! = 120$ ways.Now the group C has 3 elements, they can be arranged in $3! = 6$ ways.Hence by multiplication principle, required number of words = $2! \times 5! \times 3!$the total no of ways = $1440$Therefore, 1440 words with or without meaning, can be formed using all the letters of the word ‘EQUATION’, at a time so that the vowels and consonants occur together. Note: Always keep an eye on the keywords used in the question. The keywords can help you get the answer easily. The keywords like-selection, choose, pick, and combination-indicates that it is a combination question.Keywords like-arrangement, ordered, unique- indicates that it is a permutation question.If keywords are not given, then visualize the scenario presented in the question and then think in terms of combination and arrangement.Last updated at May 29, 2018 by Teachoo
Support Teachoo in making more (and better content) - Monthly, 6 monthly, yearly packs available! Ex 7.3, 8 How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter Exactly once? Number of letters in word EQUATION` = 8 n = 8 If all letters of the word used at a time r = 8 Different numbers formed = nPr = 8P8 = 8!/(8 8)! = 8!/0! = 8!/1 = 8! = 8 7 6 5 4 3 2 1 = 40320 Next: Ex 7.3,9 Important → Get the answer to your homework problem. Try Numerade free for 7 days Catherine T. Algebra 8 months, 3 weeks ago We don’t have your requested question, but here is a suggested video that might help. How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once? How many different arrangements can be made from the letters of the word EQUATION?Therefore, 1440 words with or without meaning, can be formed using all the letters of the word 'EQUATION', at a time so that the vowels and consonants occur together.
How many different arrangements can be formed from the letters of the word EQUATION of each arrangement begins and ends with a consonant?Hence, we can form a total 4320 different words ending and beginning with consonants with the letters of the word EQUATION.
How many different arrangements can be formed of the word EQUATION if all the vowels are kept together?How many words can be formed by the word "equation" keeping the vowels together? Put the vowels (euaio) together - there are 5!= 120 such arrangements.
How many arrangements of letters are there in math?The word MATHEMATICS consists of 2 M's, 2 A's, 2 T's, 1 H, 1 E, 1 I, 1 C and 1 S. Therefore, a total of 4989600 words can be formed using all the letters of the word MATHEMATICS.
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