Aptitude Day 115

Problems On Permutations and Combinations:

1. How many 3-letter words with or without meaning, can be formed out of the word, 'MOTHER' if repetition is not allowed?

Solution:
                 The word MOTHER has 6 letters and we should form 3-letter words. Hence,

                 ⁶P3 = 6!/ (6-3)!
                        = 6*5*4*3!/3!
                        = 120. 

2. How many words with or without meaning, can be formed by using all the letters of the word, 'MOTHER' using each letter exactly once?

Solution:
                The word MOTHER has 6 letters. Hence,

                 ⁶P6 = 6! = 720.