Find the number of ways to arrange the letters of the word 'SANKRANTI' so that all the vowels always

M4maths Previous Puzzles

14 Jan 2022 Permutation and Combination

Find the number of ways to arrange the letters of the word 'SANKRANTI' so that all the vowels always occur together.

OPtion

1) 90720
2) 10080
3) 15120
4) 22680
5) 30240
6) 11340
7) 7560
8) 8480
9) 6420
10) None of these

Solution

In a 9 letter word SANKRANTI, there are 3 vowels i.e. two A's and one I.
Any group of letters can be arranged in n!/(P1!*P2!*..) ways, where n=Total letters and P1, P2 are number of repetitions.
We have to arrange SNKRNT (AAI) considering it a 7 letters word, where N repeats twice.
Now, these 7 letters can be arranged in 7!/2! ways with 2 repetition of N.
Vowels AAI can be arranged among themselves in 3!/2! ways with 2 repetition of A.
Hence, total number of arrangements = (7!/2!)*(3!/2!) = 7560

Correct Option: 7 Best Solution (0)