# GMAT Quant Practice | Permutation Q2

#### Rearrangement and Reordering | Permutation Combination

This GMAT quant practice question is a counting methods problem solving question. The concept tested in this question is to find the number of ways a few letters from a word can be selected and rearranged such that the rearrangement adheres to a specified constraint.

Question 2: How many different four letter words can be formed (the words need not be meaningful) using the letters of the word MEDITERRANEAN such that the first letter is E and the last letter is R?

1. 59
2. $$frac{11!}{2!×2!×2!}$ 3. 56 4. 23 5. $\frac{11!}{3!×2!×2!×2!}$ ## Get to 705+ in the GMAT #### Online GMAT Course @ INR 8000 + GST ### Video Explanation ## GMAT Live Online Classes #### Starts Sat, July 20, 2024 ### Explanatory Answer | GMAT Combinatorics | Reordering Q2 #### Step 1 of solving this GMAT Permutation Question: Select 2 letters and rearrange them MEDITERRANEAN is a 13-letter word. We have to form a 4-letter words that start with 'E' and ends with 'R'. Therefore, in addition to E and R, we have to find two more letters from the remaining 11 letters. In these 11 letters, there are 2 Ns, 2Es, and 2As and one each of the remaining 5 letters viz., M, D, I, T, and R. #### Step 2 of solving this GMAT Permutation Question: List down the different posssibilities Of the 11 letters, there are 2 Ns, 2Es, and 2As and one each of the remaining 5 letters. The second and third positions can either have two different letters or can both be the same letters. Case 1: When the two letters are different We have to choose two different letters from the 8 available different choices. This can be done in 8 × 7 = 56 ways. Case 2: When the two letters are same There are 3 options - the two letters can be Ns or Es or As. Therefore, 3 ways. Total number of posssibilities = 56 + 3 = 59 #### Choice A is the correct answer. #### GMAT Online CourseTry it free! Register in 2 easy steps and Start learning in 5 minutes! #### Already have an Account? #### GMAT Live Online Classes Next Batch July 20, 2024 Work @ Wizako ##### How to reach Wizako? Mobile:$91) 95000 48484
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