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?
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.
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
1. GMAT Permutation Combination Practice | 600 level PS question | Rearranging letters
2. GMAT Permutation Practice Question | 650 to 700 level question | Selecting & Rearranging Letters
3. GMAT Probability Practice Question | 600 level | Rearranging letters of a word
4. GMAT Probability Practice Question | 650 to 700 Level Question | Counting Methods
5. GMAT Probability Practice | Mutually Exclusive Collectively Exhaustive Events
6. GMAT Permutation Practice Question | Sampling with replacement
7. GMAT Permutation Sample Question | GMAT Coin Toss | GMAT 600 Level Question Permutation Combination
8. GMAT Permutation Combination | GMAT Sample Questions | GMAT 600 Level Practice Question
9. GMAT Permutation Combination | GMAT Sample Questions | GMAT 600 to 650 Level Practice Question
10. GMAT Permutation and Probability | GMAT Data Sufficiency | GMAT 700 Level Sample Questions
11. Selecting From Identical Objects | GMAT Permutation and Probability | GMAT Sample Questions
12. GMAT Permutation and Probability | GMAT 600 to 650 level | GMAT Sample Questions
13. GMAT Permutation Combination and Probability | Numbers & Digits | GMAT Sample Questions | 650 level
14. GMAT Permutation Combination and Probability | Numbers & Digits | GMAT 650 to 700 level Questions
15. GMAT Permutation Combination | Tossing Coins | 650 Level Practice | Online Preparation
GMAT® is a registered trademark of the Graduate Management Admission Council (GMAC). This website is not endorsed or approved by GMAC.
GRE® is a registered trademarks of Educational Testing Service (ETS). This website is not endorsed or approved by ETS.
SAT® is a registered trademark of the College Board, which was not involved in the production of, and does not endorse this product.
Wizako - GMAT, GRE, SAT Prep
An Ascent Education Initiative
14B/1 Dr Thirumurthy Nagar 1st Street
Chennai 600 034. India