Aptitude Day 118

Problems on Permutations and Combinations:

1. How many arrangements can be made out of the word 'ENTREPRENEUR'?

Solution:
               The given word has 12 letters and E is repeated 4 times, N is repeated twice and R is repeated thrice. Hence,

                12! / 4! 2! 3! = 1663200.

2. How many words can be formed from the letters of the word 'VOLUME' so that the vowels always come together?

Solution:
               The arrangement will be VLM (OUE)

               The 4 letters can be arranged in 4! = 24.
               The vowels can be arranged among themselves in 3! = 6.

               The required number of ways = 24*6 = 144.