Aptitude day 112

Problems on Permutations and Combinations:

1. How many words can be formed by using all letters of the word 'POLICE'?

Solution:
               The word POLICE contain 6 different letters.
               ⁶P6 = 6! = 6*5*4*3*2*1 = 720.

2. How many words can be formed by using all letters of the word 'TIME' so that the vowels always come together?

Solution:
                The word contains 4 different letters. When the vowels always come together, we may treat that whole entity as 1 letter.

                The letters to be arranged are TM (IE).

                These 3 letters can be arranged in ³P3 = 3! = 6 ways.

                The vowels in (IE) may be arranged in 2! = 2 ways.

                The required number of words = 6*2 =  12.