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
Register in 2 easy steps and
Start learning in 5 minutes!
Next Batch April 9, 2023
GMAT Questionbank | Number Properties
GMAT Math Questions | Inequalities
GMAT Math Questions | Set Theory
GMAT Questions | Ratio, Percent, Fractions
GMAT Sample Questions | Rates - Work, Speed
GMAT Questions | Permutation & Probability
GMAT Sample Questions | Geometry
Copyrights © 2016 - 23 All Rights Reserved by Wizako.com - An Ascent Education Initiative.
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
Mobile: (91) 95000 48484
WhatsApp: WhatsApp Now
Leave A Message
TANCET Previous Year Question Papers
NCERT Solution for Class 10 Maths
CBSE Sample Papers for class 10