The word ARRANGEMENT has $11$ letters, not all of them distinct. Imagine that they are written on little Scrabble squares. And suppose we have $11$ consecutive slots into which to put these squares. There are $\dbinom{11}{2}$ ways to choose the slots where the two A's will go. For each of these ways, there are $\dbinom{9}{2}$ ways to decide where the two R's will go. For every decision about the A's and R's, there are $\dbinom{7}{2}$ ways to decide where the N's will go. Similarly, there are now $\dbinom{5}{2}$ ways to decide where the E's will go. That leaves $3$ gaps, and $3$ singleton letters, which can be arranged in $3!$ ways, for a total of $$\binom{11}{2}\binom{9}{2}\binom{7}{2}\binom{5}{2}3!.$$
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In how many ways can be letters of the word MULTIPLE be arranged [#permalink]
M U L T I P L E, has 8 letters, with 5 consonants (L repeated twice) and 3 Vowels.U I and E should not change their order, but can change positions. 3 positions can be chosen out of 8 in 8C3 = 56 waysThe remaining 5 consonants can be arranged in 5!/2! = 5 * 4 * 3 = 60 waysThe total number of ways = 56 * 60 = 3360 Option E Arun Kumar _________________
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Re: In how many ways can be letters of the word MULTIPLE be arranged [#permalink]
CrackVerbalGMAT wrote: M U L T I P L E, has 8 letters, with 5 consonants (L repeated twice) and 3 Vowels.The Vowels in the 2nd, 5th and 7 places. These can be arranged in 3! = 6 ways.The remaining 5 consonants can be arranged in 5!/2! = 5 * 4 * 3 = 60 waysThe total number of ways = 6 * 60 = 360 Option C Arun Kumar CrackVerbalGMAT Could the question also mean that the vowels remain fixed in their places? If thats the case the answer would be 60. I understand your POV as well, but I feel it would be clearer if it said something like vowels's relative position to the consonants is fixed.
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Re: In how many ways can be letters of the word MULTIPLE be arranged [#permalink]
Brian123 wrote:
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Re: In how many ways can be letters of the word MULTIPLE be arranged [#permalink]
CrackVerbalGMAT wrote: Brian123 wrote:
Order normally means position. If the vowels were to remain in the same position as they were, then the question would have made that clear. For eg it would or should have stated that the order of the vowels and the Vowels remain unchanged.Arun Kumar The highlighted part is what lead me to the believe that the vowels would remain fixed. Also, I'm pretty sure I've seen a question which said that "the vowels's relative position to the consonants is fixed".
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Re: In how many ways can be letters of the word MULTIPLE be arranged [#permalink]
CrackVerbalGMAT wrote: M U L T I P L E, has 8 letters, with 5 consonants (L repeated twice) and 3 Vowels.The Vowels in the 2nd, 5th and 7 places. These can be arranged in 3! = 6 ways.The remaining 5 consonants can be arranged in 5!/2! = 5 * 4 * 3 = 60 waysThe total number of ways = 6 * 60 = 360 Option C Arun Kumar You're right, no changing the order of the vowels means that U I E should be in the same order, but can have different positions. The answer in this case will not be 60 or 3360. Have made the relevant changes in the post.Arun Kumar _________________
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In how many ways can be letters of the word MULTIPLE be arranged [#permalink] Vowels together but order same: MLTPL(UIE) = 6! /2! = 720 / 2 = 360 ['L' being twice so 2!] Answer C _________________
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Re: In how many ways can be letters of the word MULTIPLE be arranged [#permalink] MathRevolutionYour method indicates option C (360) but you have chosen E (3360). What is the correct answer?If it is E then what is the correct approach? Am I missing something? Quote: Vowels together but order same: MLTPL(UIE) = 6! /2! = 720 / 2 = 360 ['L' being twice so 2!] Answer E _________________
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Re: In how many ways can be letters of the word MULTIPLE be arranged [#permalink] It looks like the question can be interpreted in many ways. Perhaps the author/source/experts can decide how to proceed with this.
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Re: In how many ways can be letters of the word MULTIPLE be arranged [#permalink] Question says that without changing the vowels. So separate the vowels from the word.MLTPL(consonants) UIE(vowel)Now there are 5 consonants, in which L is repeated 2 times.Similarly, we can consider UIE as 1 unit of vowel only, as we cannot shuffle this.Hence total 5 consonants + 1 vowel = 6.6!/2! = 360Therefore ans should be C Posted from my mobile device
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Re: In how many ways can be letters of the word MULTIPLE be arranged [#permalink]
Brian123 wrote: CrackVerbalGMAT wrote: Brian123 wrote:
Order normally means position. If the vowels were to remain in the same position as they were, then the question would have made that clear. For eg it would or should have stated that the order of the vowels and the Vowels remain unchanged.Arun Kumar The highlighted part is what lead me to the believe that the vowels would remain fixed. Also, I'm pretty sure I've seen a question which said that "the vowels's relative position to the consonants is fixed". The question only talks about the relative order of vowels, not their position. The question that you are referring to is here: https://gmatclub.com/forum/in-how-many- ... 48806.html
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Re: In how many ways can be letters of the word MULTIPLE be arranged [#permalink]
rsrighosh wrote: MathRevolutionYour method indicates option C (360) but you have chosen E (3360). What is the correct answer?If it is E then what is the correct approach? Am I missing something? Quote: Vowels together but order same: MLTPL(UIE) = 6! /2! = 720 / 2 = 360 ['L' being twice so 2!] Answer E Hello,Thank you for catching that typo error. I have made the changes. Answer si C - 360.Thanks _________________
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Re: In how many ways can be letters of the word MULTIPLE be arranged [#permalink] Here is what I did:(1) There are 8! ways we can rearrange the letters. Since "L" appears twice, the total number will -> 8!/2!(2) I determined the number of ways the vowels can be rearranged. Since there are 3 vowels, therefore, there are 3! ways these vowels can be rearranged.Since we do not want the vowels to be rearranged, therefore, we can say that 1 out of 3! times the vowels will NOT be rearranged. So we multiply 1/3! to the total of ways we can rearrange the letters. -> 8!/3!2! -> 3360
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Re: In how many ways can be letters of the word MULTIPLE be arranged [#permalink]
Re: In how many ways can be letters of the word MULTIPLE be arranged [#permalink] 27 May 2022, 02:01 |
In how many other ways can the letters of the word multiple be arranged
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