Aptitude Day 120

Problems on Permutations and Combinations:

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

Solution:
               The arrangement will be PWR (OE)

               The 4 letters can be arranged in 4! = 24.
               The vowels can be arranged among themselves in 2! = 2.

               The required number of ways = 24*2 = 48.

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

Solution:
               The arrangement will be SGNL (IA)

               The 5 letters can be arranged in 5! = 120.
               The vowels can be arranged among themselves in 2! = 2.

               The required number of ways = 120*2 = 240.