Permutation and Combination - Sample Question for Permutation

Sample Question A:

-   How many ways or permutation are there of the letters of the word “RAINBOW”?

Answer:

 

Sample Question B:

-   There are 8 different type of color of book in the bookshelf. How many ways can 8 books are arranged on a bookshelf?

Answer: 

Sample Question C:

-   Find the number of permutations of all the letters in the word. Find the number of the permutations in which

                               i.            The letters U and D are together,

                              ii.            The letters U and D are not together.

Answer:

          i.  To ensure that U and D are together, we gather them to form one block. Within this block the letters can be permuted in 2! ways. This block with the remaining 5 letters from 6 object which can be permuted in 6! ways. Hence by the basic counting principle,

                     

         ii.  The number of permutation in which U and D are not together = total number of permutations without restrictions – the number of permutations with U and D together =  3600