Find The Number Of Arrangement That Can Be Made Of The Letters Of The Word Hexagon.docx

Find the number of arrangement that can be made of the letters of the word HEXAGON, so that the vowels may not be in consecutive positions in any one of them. 1440 Find the total number of permutation of the letters of the word VALEDICTORY taken at all at a time, so that the vowels never come together. 8467200 In how many other ways the letters of the word TRIANGLE be arranged (i) (ii) (iii)

Without changing the order of the Vowels, Keeping the position of the vowels fixed and Without changing the relative order of the vowels and consonants.

3359, 59, 359

The word TRIANGLE has total 11 characters. Out of them, 3 are Vowels ( I A E) occupying positions 3, 4, 8 5 are consonants ( T R N G L) occupying positions 1,2,5,6,7 Relative order of vowels and consonants cannot be changed. i.e., position of vowels and consonants cannot be changed 3 vowels can be arranged in 3! ways 5 consonants can be arranged in 5! ways Total number of ways = 5!3!=720 In how many ways can the letters of the word UTILITARIANTSM be rearranged without changing the relative order of vowels and consonants. 264599 In the word ALGEBRA, there are three vowels (A, A and E) and four consonants (L, G, B and R)

We need to find different arrangements of the word ALGEBRA such that relative positions of vowels and consonants do not change.

Therefore, in the three positions occupied by vowels, we can rearrange the vowels in 3!/2! = 3 ways.

Four consonants can be rearranged in four spaces occupied by consonants in 4! ways = 24 ways.

Therefore, required number of arrangements = 3 x 24 = 72.

Read more on Brainly.in - https://brainly.in/question/1088276#readmore Find the total number permutation of the letter of the word RATIONALISATION. In how many of them will first three position be occupied by 3 ‘I’s and the last two by the 2 ‘t’s ? 45405360 & 151200

On how many ways can the letters of the word "COMPUTER" be arranged? 1. Without any restrictions: Since all letters in the word "COMPUTER" are distinct then the # of arrangements is 8!. 2. M must always occur at the third place: M is fixed at the third place, other 7 distinct letters can be arranged in 7! ways, 3. All the vowels are together: Consider three vowels as one unit: {OEU}. Thus we'll have total of 6 units: {OEU}{C}{M}{P}{T}{R}, which can be arranged in 6! ways. Three vowels within their unit can be arranged in 3! ways. Total: 6!*3!. 4. All the vowels are never together: Total minus restriction: 8!-6!*3!. 5. Vowels occupy the even positions (the vowels can occupy only even positions): C|O|M|P|U|T|E|R O|E|O|E|O|E|O|E (O and E stand for odd and even positions respectively). # of arrangements would be C34∗3!∗5!=4!∗5!=2880C43∗3!∗5!=4!∗5!=2880.

C34C43 - 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); 3!3! - # of different arrangements of these vowels on their even positions; 5!5! - # of different arrangements of 8-3=5 other letters left. Hope it helps. _________________ New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets |PDF of

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Most Helpful Community Reply grad_mba Director

Re: In how many ways can the letters of the word "COMPUTER" be arranged? [#permalink] 25 2007, 18:39

4 1 1 3) All vowels are together -

Joined: 13 Mar 2007 Posts: 530 Schools: MIT Sloan

C-O-M-P-U-T-E-R has 3 vowels - for th be together, consider them as a single en K,

so now we have 6 alphabets (C,M,P,T,R ways

K comprises of 3 alphates - so K can arr itself in 3! ways,

hence total 6! x 3!

5) There are 4 even positions to be filled vowels -so by direct counting 4 x 3 x 2

remaining 5 positions are occupied by th alphabets in 5! ways => 5! x 4!

General Discussion grad_mba Director

Re: In how many ways can the letters of the word "COMPUTER" be arranged? [#permalink] 25 2007, 13:33

2 1) 8! 2) 7! 3) 6! x 3! 4) 8! - [6! x 3!] 5) 4! x [4x3x2]

Joined: 13 Mar 2007 Posts: 530 Schools: MIT Sloan

ankita Manager

Re: In how many ways can the letters of the word "COMPUTER" be arranged? [#permalink] 26 2007, 08:53

1

Thank you. somehow i can't be sure of m answers, when it comes to arrangement possibilities or probability calculation. T i got first 4 correct here

Joined: 17 Apr 2007 Posts: 85

vijay2001 Manager

Re: In how many ways can the letters of the word "COMPUTER" be arranged? [#permalink] 26 2007, 11:00

1 4) All the vowels are never together

Does this mean, they are all seperate? If the questions, then asnwer is 4! 5P3 way

Joined: 28 Aug 2006 Posts: 152

BDSunDevil Manager

Re: In how many ways can the letters of the word "COMPUTER" be arranged? [#permalink] 14 2011, 10:43

1

Can someone check for 4 and 5: i keep g 4: 5!*6p3=2400 5. 720*4=2880

Joined: 13 May 2011 Posts: 222 WE 1: IT 1 Yr WE 2: Supply Chain 5 Yrs

Chembeti Manager

Re: In how many ways can the letters of the word "COMPUTER" be arranged? [#permalink] 19 2012, 03:07

4 BDSunDevil wrote:

Can someone check for 4 and 5: i ke getting 4: 5!*6p3=2400 5. 720*4=2880

Joined: 25 Nov 2011 Posts: 164 Location: India Concentration: Technology, General Management GPA: 3.95 WE: Information Technology (Computer Software)

4) All the vowels are never together. This is equivalent to (All possibilities - A vowels are ALWAYS together) = 8! - 6

5) Vowels occupy the even positions. let us consider the following: first 3 vow placing together in even positions: -O-U-E--O---U-E ---O-U-E Like this, at any point in time we have 4 positions to fill with 3 letters. Hence no. ways will be 4P3 = 4!

Remaining 5 positions can be filled by 5 Hence total ways = 4! x 5!

Hope this is clear. (if you like, give me k please ) _________________ -------------------------Aravind Chembeti

Apex231 Intern

Re: In how many ways can the letters of the word "COMPUTER" be arranged? [#permalink] 19 2012, 18:33

1 Joined: 03 Oct 2009 Posts: 49

4. All the vowels are never together: I did this 3 vowels and 5 non-vowels.

number of ways to arrange 5 non-vowel (represented by | below). -|-|-|-|-|-

Now there are 6 places (represented by vowels can occupy so that they are not together. Number of ways vowels can be arranged = 120

total number of ways = 120 * 5! = 1440 What am i doing wrong?

Chembeti Manager

Re: In how many ways can the letters of the word "COMPUTER" be arranged? [#permalink] 19 2012, 20:24

2 Apex231 wrote:

4. All the vowels are never together I did this 3 vowels and 5 non-vowels. Joined: 25 Nov 2011 Posts: 164 Location: India Concentration: Technology, General Management GPA: 3.95 WE: Information Technology (Computer Software)

number of ways to arrange 5 non-vo 5! (represented by | below). -|-|-|-|-|-

Now there are 6 places (represented

that vowels can occupy so that they not together.

Number of ways vowels can be arra 6P3 = 120

total number of ways = 120 * 5! = 14

What am i doing wrong?

Question says "ALL the vowels not tog So, you have excluded valid cases like COMPTUER, CMPOUTER

One thing: it is generally a good practice find the probability of something to occ then subtract it from 1 to find for the sam thing to not occur. This way, we don;t c above mistakes. Kudos please, if this is clear _________________ -------------------------Aravind Chembeti

docabuzar Intern

Re: In how many ways can the letters of the word "COMPUTER" be arranged? [#permalink] 19 2012, 23:43

1 1. 8! 2. 7! 3. 6! x 6 4. 8! - (6!x6) 5. 5! x (4C3)

Joined: 17 Jan 2012 Posts: 41 GMAT 1: 610 Q43 V31

Bunuel Math Expert

Re: In how many ways can the letters of the word "COMPUTER" be arranged? [#permalink] 19 2012, 23:46

1

docabuzar wrote:

1. 8! 2. 7! 3. 6! x 6 4. 8! - (6!x6) 5. 5! x (4C3)

V Joined: 02 Sep 2009 Posts: 53560

Answer for question #5 is not correct, it be 5!*4!. Check the solutions above and anything remains unclear. _________________

New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEA READ AND FOLLOW: 12 Rules for Posting!

Resources: GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets |PD Math Book; 10. Remainders | GMAT Prep So Analysis | SEVEN SAMURAI OF 2012 (BES DISCUSSIONS) | Tricky questions from prev years.

Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard qu 3. Hard questions part 2; 4. Standard deviation 5. Tough Problem Solving Questions With So 6. Probability and Combinations Questions W Solutions; 7 Tough and tricky exponents and r questions; 8 12 Easy Pieces (or not?); 9 Baker Dozen; 10 Algebra set. ,11 Mixed Questions, 1 Meat

DS: 1. DS tough questions; 2. DS tough questi 2; 3. DS tough questions part 3; 4. DS Standar deviation; 5. Inequalities; 6. 700+ GMAT Dat Sufficiency Questions With Explanations; 7 T and tricky exponents and roots questions; 8 Th Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.

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docabuzar Intern

Re: In how many ways can the letters of the word "COMPUTER" be arranged? [#permalink] 20 2012, 12:40

Bunuel wrote: docabuzar wrote:

1. 8! 2. 7! 3. 6! x 6 4. 8! - (6!x6) 5. 5! x (4C3) Joined: 17 Jan 2012 Posts: 41 GMAT 1: 610 Q43 V31

Answer for question #5 is not correc

should be 5!*4!. Check the solutions

and ask if anything remains unclear

Thanks for correction. I intended to write 5! x (4P3) => 5! x 4! I m worried, the time pressure never cea cause such mistakes!

AniDroid Intern

Re: In how many ways can the letters of the word "COMPUTER" be arranged? [#permalink] 10 2016, 22:46

For the 5th question-

There are 8 available places in the word COMPUTER. 5 Consonants and 3 Vow

Joined: 03 Aug 2012 Posts: 1 Location: India Concentration: Technology, Healthcare GMAT 1: 700 Q51 V34

GPA: 3.65 WE: Project Management (Manufacturing)

First choose 4 consonants to be filled in positions in 5P4 ways = 120

Then 4 balance alphabets, including the vowels, can be filled in 4 even positions ways = 24

Total number of ways = 120*24 = 2880