Question
If all words with 2 distinct vowels and 3 distinct consonants were listed alphabetically, what would be the rank of “ACDEF’?
A. 4716
B. 4720
C. 4718
D. 4717
Correct Answer
Choice C
Explanatory Answer
The first word would be ABCDE. With 2 distinct vowels, 3 distinct consonants, this is the first word we can come up with.
Starting with AB, we can have a number of words
AB __ __ __. The next three slots should have 2 consonants and one vowel. This can be selected in 20C2and 4C1 ways. Then the three distinct letters can be rearranged in 3! Ways.
Or, number of words starting with AB = 20C2* 4C1 * 3! = 190 * 4 * 6 = 4560
Next, we move on to words starting with ACB
ACB __ __. The last two slots have to be filled with one vowel and one consonant. = 19C1 * 4C1. This can be rearranged in 2! Ways.
Or, number of words starting with ACB = 19C1 * 4C1* 2 = 19 * 4 * 2 = 152
Next we move on words starting with ACDB: There are 4 different words on this list – ACDBE, ACDBI, ACDBO, ACDBU
So, far number of words gone = 4560 + 152 + 4 = 4716
|
Starting with AB
|
4560
|
|
Starting with ACB
|
152
|
|
Starting with ACDB
|
4
|
|
Total words gone
|
4716
|
After this we move to words starting with ACDE, the first possible word is ACDEB. After this we have ACDEF.
So, rank of ACDEF = 4718
Answer Choice (C)
Related posts
October 10, 2014 CAT Permutation and Combinations Question
If we list all the words that can be formed by rearranging the letters of the word SLEEPLESS in alphabetical order, what would be the rank of […] Posted in Combinatorics- October 23, 2014 CAT Preparation Online – Tough one from Permutation and Combination
Question
A wonderful, but very tough question from Permutation and Combinations.
In how many ways, can we rearrange the word MONSOON such that no two adjacent positions are […] Posted in Combinatorics
- April 29, 2015 CAT Online Coaching – Permutation and Combination, Fixing the Errors III
This post had given a series of questions with incorrect solutions. Given below are the "debugged" solutions to questions 7, 8 and 9.
7. What is the probability of selecting 3 […] Posted in Combinatorics
- July 26, 2016 CAT Permutation Combination – Online Prep for CAT 2016 CAT Permutation Combination: In how many ways can the letters of the word EDUCATION be rearranged such that the order in which the vowels appear in the word doesn't change?
This is a […] Posted in Uncategorized