In how many ways can be letters of the word MULTIPLE be arranged

Question

In how many ways can be letters of the word MULTIPLE be arranged without changing the order of the vowels ?

A. 60
B. 90
C. 360
D. 1860
E. 3360

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CrackverbalGMAT · Accepted Answer

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 ways

The remaining 5 consonants can be arranged in 5!/2! = 5 * 4 * 3 = 60 ways

The total number of ways = 56 * 60 = 3360

Option E

Arun Kumar

MBAB123 · Answer

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.

CrackverbalGMAT · Answer

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

MBAB123 · Answer

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".

CrackverbalGMAT · Answer

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

MathRevolution · Answer

Vowels together but order same: MLTPL(UIE) = 6! /2! = 720 / 2 = 360

Answer C

rsrighosh · Answer

MathRevolution

Your 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?

MBAB123 · Answer

It looks like the question can be interpreted in many ways. Perhaps the author/source/experts can decide how to proceed with this.

Shubham1213372 · Answer

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! = 360

Therefore ans should be C

Posted from my mobile device

Dvaishnav · Answer

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

MathRevolution · Answer

Hello,

Thank you for catching that typo error. I have made the changes. Answer si C - 360.

Thanks

smmc29 · Answer

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

Kushchokhani · Answer

MathRevolution

OA is E.

In how many ways can be letters of the word MULTIPLE be arranged

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In how many ways can be letters of the word MULTIPLE be arranged

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