CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Consider the letters of the word ARRANGE. Then the possible number of words


A
when 2Rs are not together is 5!2!× 6P2=900
loader
B
when two As are together but not two R's is 240
loader
C
when the vowels are together is 5!3!2!2!
loader
D
when both As are together and both Rs are together is 120
loader

Solution

The correct options are
B when two As are together but not two R's is 240
C when the vowels are together is 5!3!2!2!
D when both As are together and both Rs are together is 120
When 2Rs are not together.
Arrange the letters A,A,N,G,E in alternate manner, such that there will be 6 spaces left, so that can be filled by 2Rs in 6C2 ways
So the total possible words =5!2!× 6C2=900

When two As are together but not two Rs.
The number of words in which both A's are together 
=6!2! [consider both the As as one unit]
=360
The number of words in which both As and both Rs are together is 5!=120
[consider both the As as one unit and both the Rs as one unit]
Therefore, the number of words in which both As are together but the two Rs are not together is 360120=240

When the vowels are together.
Make one group of all vowels.
The total ways of arrangement is =5!×3!2!2!

When both As are together and both Rs are together.
Make one group 2As and another group of 2Rs.
The total ways of arrangement is =5!=120

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image