How many different word can be formed of the letter of the word combine so that no two vowels are together?
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Joined: 02 Sep 2009 Posts: 86772 The letters of the word PROMISE are arranged so that no two of the vow [#permalink]
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Hide Show timer StatisticsThe letters of the word PROMISE are arranged so that no two of the vowels should come together. Find total number of arrangements. A. 7 _________________ Manager Joined: 05 Oct 2017 Posts: 61 Location: India The letters of the word
PROMISE are arranged so that no two of the vow [#permalink]
Really Good Question i learned it the hard way , hope my solution helps __C__C__C__C__ But since we require only 3 places due to 3 vowels to be arranged so we will select the 3 places out of 5 in 5C3 ways = 10 ways In the given arrangement the Consonants can be arranged in 4! Ways at the selected 4 places and, All the vowels can also be arranged among themselves in 3! Ways so Total ways to arrange the letters as per desired condition = 10*3!*4! = 1440 Answer: Option C Manager Joined: 08 Jan 2013 Posts: 81 Re: The letters of the word
PROMISE are arranged so that no two of the vow [#permalink]
This can also be solve as an overlapping set problem - Ans C. GMAT Club Legend Joined: 18 Aug 2017 Status:You learn more from failure than from success. Posts: 7204 Location: India Concentration: Sustainability, Marketing GPA: 4 WE:Marketing (Energy and Utilities) Re: The letters of the word PROMISE are arranged so that no two of the vow [#permalink]
Bunuel wrote: The letters of the word PROMISE are arranged so that no two of the vowels should come together. Find total number of arrangements. A. 7 Combine vowels together so we are left with 4 places for Consonants and 1 for vowels out of 7 we will have now 4+1 = 5 ways and since 3 vowels are given then the combination to arrange this array is 5c3 Intern Joined: 19 Jul 2018 Posts: 12 Re: The letters of the word PROMISE are arranged so that no two of the vow [#permalink]
Let '__' denote the possible locations of the vowels in the resultant word. Since no two vowels can be together, there must be at least one consonant between them. __C1__C2__C3__C4__ Number of ways in which consonants can rearrange among themselves = 4! = 24 ways Now, we have 5 different spots that can accommodate vowels. We have 5 spots; we need 3. Does order of appearance of vowels matter? Of course! Since we have to count possible arrangements here, order does matter. Therefore number of ways of choosing 3 spots from a pool of 5 (for our vowels) is 5P3 = 5!/2! = 60. Therefore total number of ways in which the acceptable arrangements can be achieved = 24*60 = 1440 ways Best Regards, Manager
Joined: 30 May 2019 Posts: 161 Location: United States Concentration: Technology, Strategy GPA: 3.6 Re: The letters of the word PROMISE are arranged so that no two of the vow [#permalink]
Bunuel wrote: The letters of the word PROMISE are arranged so that no two of the vowels should come together. Find total number of arrangements. A. 7 I have two solutions I wanted to share. 1. Using straight calculation We know the set of consonants = C = {P, R, M, S} and set of vowels = V = {O, I, E}. Since no vowels should come together, all the consonants are placed in between them, or they form the start and end of the word. Hence the format for the acceptable answer is : _ C _ C _ C _ C _ Talking about the vowels, we have 3 vowels and 5 place for them. So we have to pick 3 positions where we can put those 3 vowels. Hence total no. of ways is : 4 ! * 5C3 * 3 ! = 1440 2. Using negation no. of ways so that no two of the vowels are together = total no of ways - no. of ways so all 3 vowels are together - no. of ways so 2 of the vowels are together total no. of ways we can find when 3 vowels are together : total no. of ways we can find when 2 vowels are together : So 7! - 5!*3! - (3C2 * 5C1 * 2! * 4) = 1440 I know 2nd option becomes cumbersome but was a great exercise in thinking through different way to do the problem. Non-Human User Joined: 09 Sep 2013 Posts: 24427 Re: The letters of the word PROMISE are arranged so that no two of the vow
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Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. Re: The letters of the word PROMISE are arranged so that no two of the vow [#permalink] 13 Jun 2021, 09:18 Moderators: Senior Moderator - Masters Forum 3084 posts How many different words can be formed of the letters of the word combine no two vowels are together?Re the COMBINE puzzle where we want to know the number of combinations where no two vowels occur together. I did it the long way using an Excel spreadsheet and the answer is 1440. There are 5040 possible combinations.
How many different words can be formed of the letters of the word combine so that vowels may occupy odd places?In order that the vowels may occupy odd places, we first of all arrange any 3 consonants in even places in 4P3 ways and then the odd places can be filled by 3 vowels and the remaining 1 consonant in 4P4 ways. So, Required number of words = 4P3 × 4P4 = 24 × 24 = 576.
How many different words can be formed using all the letters of the word combine?Words that can be made with combine
64 words can be made from the letters in the word combine.
How many ways can the letter of the word fraction be arranged so that no two vowels are together?Fraction consists of 8 letters which has 3 vowels (a, I, o) and rest 5 are consonants. It can be -F- R- C- T- N so that no 2 vowels are together. Now 3 vowels can fill these 6 places in (6,3) ways.
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