Aptitude Day 121

Problems on Permutations and Combinations:

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

Solution:
               The arrangement will be SCCD (UEE)

               The 5 letters can be arranged in 5!/2! = 120/2 = 60.
               The vowels can be arranged among themselves in 3!/2! = 6/2= 3.

               The required number of ways = 60*3 = 180.

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

Solution:
               The arrangement will be MMNT (OE)

               The 5 letters can be arranged in 5!/2! = 120/2 = 60.
               The vowels can be arranged among themselves in 2! = 2.

               The required number of ways = 60*3 = 180.