Permutations and combinations - Quantitative Aptitude (MCQ) questions for Q. 93

Q.  In how many ways can the letters of the word ENCYCLOPAEDIA be arranged such that vowels only occupy the even positions?
- Published on 15 Jun 15

a. 453600
b. 128000
c. 478200
d. 635630

ANSWER: 453600
 
This is a simple problem of permutation and combination.

Let us consider the number of times each alphabet is being used:

E: 2
N: 1
C: 2
Y: 1
L: 1
O: 1
P: 1
A: 2
I: 1
D: 1

Now, total number of consonants: 7

=> Total number of vowels: 6
13 letter word ENCYCLOPAEDIA has 6 vowels and there are 6 even spaces

=>6 vowels can be arranged in 6 spaces in 6C6*6!/(2!*2!) ways.

=>Rest of the letters (consonants) can be arranged in 7 spaces in 7C7*(7!/2!) ways

Hence total number of cases: 6!*7!/(2!*2!*2!)

=>Answer: 453600

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