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avatar+11847 

find the no. of 6 letter words that can be formed using letters of the word SQUARE such that

 

1.U and A always appear together.

 

2. U, A and R appear together.

rosala  Feb 6, 2018
 #1
avatar
0

Must it be "UA", or is "AU" acceptable as well ???

The same for "UAR", or are other perumations allowed such as "AUR", "RUA"......etc.??

Guest Feb 6, 2018
edited by Guest  Feb 6, 2018
edited by Guest  Feb 6, 2018
edited by Guest  Feb 6, 2018
 #2
avatar+87691 
+1

1.

 

Consider  "UA"  to be a single entity

 

Can  put these in any one of 5 positions    12, 23, 34, 45, 56

 

And for each of these, there are 4!  ways to arrange the other letters

 

But....we can also write UA  as AU

 

So.....the number of total "words"  is

 

2 ways to arrange UA  x  5 positons  x 4! arrangements of the other letters

 

2   x  5  x  4!   =

 

2 x  5  x  24  =

 

240  "words"

 

 

2.  

 

Similarly, for   UAR,  consider this as a single entity

 

It can appear in  4 different positions    123    234    345    456

 

And for each of these, the other letters can be arranged in 3! ways

 

But....UAR  can also be arranged in 3!  ways

 

So....the total possible "words"   =   

 

4  x  3!  x 3!  =    

 

4 x 6 x 6  =

 

144  "words"

 

 

 

cool cool cool

CPhill  Feb 6, 2018
 #3
avatar+11847 
0

CPhill i have no idea about it!? 

 

#

Can  put these in any one of 5 positions    12, 23, 34, 45, 56

 

And for each of these, there are 4!  ways to arrange the other letters

#

 

what do you mean byt he first line?i thought there were 5! ways to arrange them???

 

can you pls make it a little simple....i really cant see the permutations in them....its too confusing!Thanks!

rosala  Feb 9, 2018

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