In how many different ways can the letters A, A, B GMAT Problem-Solving

Question: In how many different ways can the letters A, A, B, B, B, C, D, E be arranged if the letter C must be to the right of the letter D?

A. 1680
B. 2160
C. 2520
D. 3240
E. 3360

Answer: D

Solution and Explanation:

Approach Solution 1:
Apply the information in the question to the GMAT question at hand. These problems apply to numerous disciplines of mathematics. This question has to do with permutations and combinations. It is challenging to select the best option because of the way the options are presented. Candidates must be able to comprehend the appropriate approach to eliciting the desired response. Out of the five possible answers, there is only one that is correct.
There are eight letters total, and the letter A appears twice while the letter B appears three times. If there were no constraints, the total number of possible permutations using these letters would be: 8!/(2!3!) = 3360
Now, in half of these scenarios, D will be to the right of C, and in the other half, it will be to the left; consequently, the total answer would be 3360/2, which is 1680.
Correct option: A

Approach Solution 2:
Apply the information in the question to the GMAT question at hand. These problems apply to numerous disciplines of mathematics. This question has to do with permutations and combinations. It is challenging to select the best option because of the way the options are presented. Candidates must be able to comprehend the appropriate approach to eliciting the desired response. Out of the five possible answers, there is only one that is correct.
Permutations of n items in which P1 and P2 are identical to one another and P3 and P3 are identical to one another. Pr is identical of the same kind such that P1+P2+P3+..+Pr =n is:
n!/(P1!∗P2!∗P3!∗...∗Pr!)
The number of ways the letters in the word "gmatclub" can be arranged, for instance, is 8! as this word contains 8 DIFFERENT letters.
There are 6 letters in the word "google," and "g" and "o" are represented twice, making there a total of 6 possible permutations.
There are 9 possible permutations if there are 4 red, 3 green, and 2 blue balls in the mixture.
There are eight letters in the original query, of which A appears twice and B appears three times. There could be 3360 different ways these letters could be put together if they were allowed to do so.
Now, in half of these scenarios, D will be to the right of C, and in the other half, it will be to the left; consequently, the total answer would be 3360/2, which is 1680.
Correct option: A

Approach Solution 3:
Apply the information in the question to the GMAT question at hand. These problems apply to numerous disciplines of mathematics. This question has to do with permutations and combinations. It is challenging to select the best option because of the way the options are presented. Candidates must be able to comprehend the appropriate approach to eliciting the desired response. Out of the five possible answers, there is only one that is correct.
There are eight letters in all, with the letter B appearing three times and the letter A twice. There would be 3360 potential permutations of these letters if there were no restrictions: 8!/(2!3!)
Because D will be to the right of C in half of these situations and to the left in the other half, the total solution would be 3360/2, or 1680.
Correct option: A

“In how many different ways can the letters A, A, B" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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