Permutations and combinations - Quantitative Aptitude (MCQ) questions for Q. 41
Q. In how many ways can the letters of the word INDIA be arranged, such that all vowels are never together?- Published on 12 Jun 15a. 48
b. 42
c. 28
d. 36
ANSWER: 42
First, we find out the number of times a particular letter occurs in the given word:
2 – I
1 – A
1 – D
1 – N
=> Total number of solutions minus the number of times all three vowels are together.
Now, using the concept of permutation and combination:
=> Divide the possible combination by 2! because it occurs twice and replacing one by another will cause no difference in the word.
=> Total number of words that can be formed: 5!/2!
=> Total number of words that can be formed keeping all the vowels together: 3! 3!/2!
=> 60 – 18 = 42
