Aptitude Day 119

Problems on Permutations and Combinations:

1. In how many different ways can the letters of the word 'FINE' be arranged so that the vowels always come together?

Solution:
               The arrangement will be FN (IE)

               The 3 letters can be arranged in 3! = 6.
               The vowels can be arranged among themselves in 2! = 2.

               The required number of ways = 6*2 = 12.

2. In how many different ways can the letters of the word 'DISPUTE' be arranged so that the vowels always come together?

Solution:
               The arrangement will be DSPT (IUE)

               The 5 letters can be arranged in 5! = 120.
               The vowels can be arranged among themselves in 3! = 6.

               The required number of ways = 120*6 = 720.