How many words of three distinct letters can be formed from the letters of the word COMPUTER?
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Intern Joined: 20 Jul 2005 Posts: 21 Location: Vietnam In how many ways can the letters of the word "COMPUTER" be arranged? [#permalink]
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Hide Show timer StatisticsIn how many ways can the letters of the word "COMPUTER" be arranged? 1) Without any restrictions. Originally posted by sonfbm on 25 Jun 2007, 13:04. Edited the question. Math Expert Joined: 02 Sep 2009 Posts: 86840 Re: In how many ways can the letters of the word "COMPUTER" be arranged?
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On how many ways can the letters of the word "COMPUTER" be arranged? 1. Without any restrictions: 2. M must always occur at the third place: 3. All the vowels are together: 4. All the vowels are never
together: 5. Vowels occupy the even positions (the vowels can occupy only even positions): # of arrangements would be \(C^3_4*3!*5!=4!*5!=2880\). \(C^3_4\) - choosing which 3 even positions out of 4 will be occupied by vowels (there are 4 even positions: 2nd, 4th, 6th and 8th and only 3 vowels); Hope it helps. Senior Manager Joined: 13 Mar 2007 Posts: 371 Schools:MIT Sloan Re: In how many ways can the letters of the word "COMPUTER" be arranged? [#permalink]
3) All vowels are together - C-O-M-P-U-T-E-R has 3 vowels - for them to be together, consider them as a single entity say K, so now we have 6 alphabets (C,M,P,T,R,K) - 6! ways K comprises of 3 alphates - so K can arrange itself in 3! ways, hence total 6! x 3! 5) There are 4 even positions to be filled by 3 vowels -so by direct counting 4 x 3 x 2 remaining 5 positions are occupied by the 5 alphabets in 5! ways => 5! x 4! Senior Manager Joined: 13 Mar 2007 Posts: 371 Schools:MIT Sloan Re: In how many ways can the letters of the word "COMPUTER" be arranged?
[#permalink] 1) 8! Intern Joined: 17 Apr 2007 Posts: 26 Re: In how many ways can the letters of the word "COMPUTER" be arranged? [#permalink]
Thank you. somehow i can't be sure of my answers, when it comes to arrangement possibilities or probability calculation. Though i got first 4 correct here Manager Joined: 28 Aug 2006 Posts: 68
Re: In how many ways can the letters of the word "COMPUTER" be arranged? [#permalink]
4) All the vowels are never together Does this mean, they are all seperate? If thats the questions, then asnwer is 4! 5P3 ways Manager Joined: 13 May 2011 Posts: 154 WE 1: IT 1 Yr WE 2: Supply Chain 5 Yrs Re: In how many ways can the letters
of the word "COMPUTER" be arranged? [#permalink]
Can someone check for 4 and 5: i keep getting Manager Joined: 25 Nov 2011 Posts: 130 Location: India Concentration: Technology, General Management GPA: 3.95 WE:Information Technology (Computer Software)
Re: In how many ways can the letters of the word "COMPUTER" be arranged? [#permalink]
BDSunDevil wrote: Can someone check for 4 and 5: i keep getting 4) All the vowels
are never together. 5) Vowels occupy the even positions. Remaining 5 positions can be filled by 5! Hence total ways = 4! x 5! Hope this is clear. (if you like, give me kudos, please Intern Joined: 03 Oct 2009 Posts: 42 Re: In how many ways can the letters of the word "COMPUTER" be arranged? [#permalink]
4. All the vowels are never together: I did this - 3 vowels and 5 non-vowels. number of ways to arrange 5 non-vowels = 5! (represented by | below). -|-|-|-|-|- Now there are 6 places (represented by -) that vowels can occupy so that they are not together. total number of ways = 120 * 5! = 14400. What am i doing wrong? Manager Joined: 25 Nov 2011 Posts: 130 Location: India Concentration: Technology, General Management GPA: 3.95 WE:Information Technology (Computer Software) Re: In how many ways can the letters of the word "COMPUTER" be arranged?
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Apex231 wrote: 4. All the vowels are never together: I did this - 3 vowels and 5 non-vowels. number of ways to arrange 5 non-vowels = 5! (represented by | below). -|-|-|-|-|- Now there are 6 places (represented by -) that vowels can occupy so that they are not together. total number of ways = 120 * 5! = 14400. What am i doing wrong? Question says "ALL the vowels not together". So, you have excluded valid cases like COMPTUER, CMPOUTER One thing: it is generally a good practice to find the probability of something to occur and then subtract it from 1 to find for the same thing to not occur. This way, we don;t commit above mistakes. Kudos please, if this is clear Intern Joined: 17 Jan 2012 Posts: 40 Re: In how many ways can the letters of the word "COMPUTER" be arranged? [#permalink]
1. 8! Math Expert Joined: 02 Sep 2009 Posts: 86840 Re: In how many ways can the letters of the word "COMPUTER" be arranged? [#permalink]
docabuzar wrote: 1. 8! Answer for question #5 is
not correct, it should be 5!*4!. Check the solutions above and ask if anything remains unclear. Intern Joined: 17 Jan 2012 Posts: 40
Re: In how many ways can the letters of the word "COMPUTER" be arranged? [#permalink]
Bunuel wrote: docabuzar wrote: 1. 8! Answer for question #5 is not correct, it should be 5!*4!. Check the solutions above and ask if anything remains unclear. Thanks for correction. Intern Joined: 03 Aug 2012 Posts: 1 Location: India Concentration: Technology, Healthcare GPA: 3.65 WE:Project Management (Manufacturing)
Re: In how many ways can the letters of the word "COMPUTER" be arranged? [#permalink]
For the 5th question- There are 8 available places in the word COMPUTER. 5 Consonants and 3 Vowels. First choose 4 consonants to be filled in 4 odd positions in 5P4 ways = 120 Then 4 balance alphabets, including the vowels, can be filled in 4 even positions in 4! ways = 24 Total number of ways = 120*24 = 2880. Hope this helps. You'll never know unless you try VP Joined: 11 Aug 2020 Posts: 1405 In how many ways can the letters of the word "COMPUTER" be arranged? [#permalink]
COMPUTER is 8 distinct letters. a) No restrictions: 8! / (8 - 8)! = 8! 4C3 = 4 < --- # of ways 3 spots can be chosen (Combination) 5!/(5-5)! = 120 <--- # of ways the remaining 5 letters are arranged (Permutation) 120 x 24 = 2880 <--- # of ways you can get vowels in even positions. "Do not pray for an easy life, pray for the strength to endure a difficult one." - Bruce Lee VP Joined: 11 Aug 2020 Posts: 1405 Re: In how many ways can the letters of the word "COMPUTER" be arranged?
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In how many ways can the letters of the word "COMPUTER" be arranged? 1) Without any restrictions: 8! "Do not pray for an easy life, pray for the strength to endure a difficult one." - Bruce Lee Non-Human User Joined: 09 Sep 2013 Posts: 24409 Re: In how many ways can the letters of the word "COMPUTER" be arranged? [#permalink]
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: In how many ways can the letters of the word "COMPUTER" be arranged? [#permalink] 23 Feb 2022, 08:54 Moderators: Senior Moderator - Masters Forum 3086 posts How many 3 letter words can be formed using the letters of the word computer?Therefore there are 8×7×6=336 choice results (permutations).
How many words can be made from a computer?Originally Answered: Determine how many words can be formed using the letters of the word computer if vowels are not together? COMPUTER: ___ ___ ___ ___ ___ ___ ___ ___ 3 vowels and 5 consonants. All the permutations possible: Excel >> 'PERMUT (8;8) = 40.320.
How many unique words are formed with the letters computer?Words that can be made with computer
173 words can be made from the letters in the word computer.
How many different word of 3 letters can be formed using the letter of the word English without repetition?Hence, the no. of 3 letter words formed from the word LOGARITHMS without repetition is 720.
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