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**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

edited by Guest Feb 6, 2018

edited by Guest Feb 6, 2018

#2**+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"

CPhill
Feb 6, 2018

#3**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