How many different strings can be formed together using the letters of the word EQUATION
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 Get the answer to your homework problem. Try Numerade free for 7 days We don’t have your requested question, but here is a suggested video that might help. Related QuestionHow many different permutations can be made with the letters of the word 'CONSTANT' so that vowels are always together?
DiscussionYou must be signed in to discuss. Video Transcriptin this problem, we are given the word constant that has warbles as zero and A. And consonants as see and yes, D. And entity Yeah. eight letters in total. Now we want the Vogels to always be together. So we have 123456 I'm making only seven spaces because the mobile, which is E. Always comes together as one entity. So we have one entity, oh and six different entities of consonants. So we have seven spaces that we have to fill. So the number of ways that we can fill it is seven factorial, but since oh, a can be interchanged as A. A. Also. So we multiply it by two. No en entity. The both occurred twice. So we have to divide by two factorial twice to account for the reputation of N and D. So these are the total um rubies. It's calculated this this is nothing but seven factorial by two, which is equal to now. seven factorial is nothing with 5040. Not divided by two ways 2 5- zero. This comes as 25 does it not? So How Many Strings Can Be Formed With The Given Word : Here we are going to see some practice questions based on the concept fundamental principle of counting. How many strings can be formed with the given word - QuestionsQuestion 1 : How many strings can be formed using the letters of the word LOTUS if the word (i) either starts with L or ends with S? (ii) neither starts with L nor ends with S? Solution : (i) either starts with L or ends with S?Case 1 : Number of words starts with L, L ___ ___ ___ ___ 1st 2nd 3rd 4th 5th 1st dash --> We have 1 option (L) 2nd dash --> We have 4 options 3rd dash --> We have 3 options 4rd dash --> We have 2 options 5rd dash --> We have 1 option = 1 ⋅ 4 ⋅ 3 ⋅ 2 ⋅ 1 = 24 words Case 2 : Number of words ends with S, ___ ___ ___ ___ S 1st 2nd 3rd 4th 5th 5rd dash --> We have 1 option (S) 1st dash --> We have 4 options 2nd dash --> We have 3 options 3rd dash --> We have 2 options 4rd dash --> We have 1 options = 4 ⋅ 3 ⋅ 2 ⋅ 1 ⋅ 1 = 24 words Case 3 : Number of words starts with L and ends with S. L ⋅ 3 ⋅ 2 ⋅ 1 ⋅ S = 6 Either starts with L or ends with S = 24 + 24 - 6 = 42 words (ii) neither starts with L nor ends with S?Total number of words formed without restriction = 5! = 120 words Number of words starts with L nor S = Total number of words - Number of words either starts with L or ends with S = 120 - 42 = 78 words Question 3 : (i) Count the total number of ways of answering 6 objective type questions, each question having 4 choices. (ii) In how many ways 10 pigeons can be placed in 3 different pigeon holes ? (iii) Find the number of ways of distributing 12 distinct prizes to 10 students? Solution : (i) Each question is having 4 options.There are 4 ways to answer each question. 1st question = 4 ways 2nd question = 4 ways ......... Total number of ways = 46 (ii) In how many ways 10 pigeons can be placed in 3 different pigeon holes ? Note : If n different objects are to be placed in m places, then the number of ways of placing is mn. 10 - Number of pigeons (different things) 3 - Number of places (pigeon holes) Applying the formula mn, Total number of ways = 310 (iii) 12 - Number of prizes (different things) 10 - Number of place (students) Applying the formula mn, Total number of ways = 1012 After having gone through the stuff given above, we hope that the students would have understood "How Many Strings Can Be Formed With the Given Word". Apart from the stuff given above, if you want to know more about "How Many Strings Can Be Formed With the Given Word". Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here. Kindly mail your feedback to We always appreciate your feedback. ©All rights reserved. onlinemath4all.com How many different strings can be made from the letters 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 words can be formed using all letters of the word EQUATION using each letter exactly once?The number of words, with or without meaning, that can be formed using all the letters of the word EQUATION, using each letter exactly once is 40,320.
How many different arrangements can be formed from the word EQUATION if in each arrangement all vowels are 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 strings can be formed using the letters Lotus?Answer: 24 strings can be formed using the letters of the word LOTUS if the word either start with L or end with S.
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