Skip to main content

Aptitude Day 113

Problems on Permutations and Combinations:

1. How many words can be formed by using all letters of the word 'TIME' so that the vowels are never 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 number of words each having vowels together = 6*2 =  12.

                 The total number of words formed by using all the letters of the given word = 4! = 24.

                The number of words each having vowels never together = 24-12 = 12.
2.  How many words can be formed by using all letters of the word 'FLUTTER' so that the vowels are always together?

 Solution:
                The word has 7 letters in which T occurs twice and others are different. So the arrangement will be FLTTR (UE).

                 The number of ways of arranging these letters = 6!/2! = 360.
                 [ Note: Here 2! is used for the repeatation]

                The vowels may be arranged in 2! = 2.

                The required number of ways = 360*2 =  720.
           

                

Comments

Post a Comment

Popular posts from this blog

Vocabulary Day 60

Incur Thesaurus: Verb :  arouse            acquire, earn, gain, include, get, obtain...  Antonyms :  lose, exclude ...  Example sentences:         ·        He is incurred in that game. ·        She incurs a great knowlegde in science.        
Post a Comment
Read more

Vocabulary Day 82

Flutter Thesaurus: Verb: wave rapidly            drift, agitate, dance, flicker, fluctuate, hover, oscillate, quiver, shake, vibrate...                                           Antonyms:  stay, remain, stay . ..  Example sentences:         ·        His heart flutters when he sees his crush.  ·       That incident causes a  flutter between them. 
Post a Comment
Read more

Aptitude Day 5

Answers of Day 4 :   1. 9                                   2. 5                                   3. 9                                   4. 8 To find the unit digit in the product. This is similar to the last model where we will find the unit digit of the sum. Example: 432*459*28*48=? Solution:  2*9=18 , 8*8=64, 4*8= 32. The unit digit of the total product is 2.  Problems to solve Find the unit digit of the product in the following 1. 404*397*810*21 =? 2. 24*42*36*78 =? 3. 81*82*89 =? 4. 72*36*98*47 =? See you tomorrow friends... Check out the answers over here  Aptitude Day 6
Post a Comment
Read more