Question

In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together?

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Answer 1

@Kainui

Answer 2

Vowels, A , E , I , O , U.

Answer 3

I think the answer is D.

Answer 4

Place them all together and you can see that only 3 letters will actually move.

Answer 5

3 letters in 3 different spots.

Answer 6

Okay :) i will do this for you :)

Answer 7

first take AAU as one group so now you have to arrang with it BCS
which can be done in 4! =24 ways but the vowels can themselves be arranged in 3!/2! = 3 ways
so the number of ways =24 *3=72

Answer 8

Exactly, since the vowels are always together, you can consider the group of vowels as one whole group to be arranged as if it was one letter among the rest.

Then once you've done that, you can imagine this single group being rearranged several times per each group. Ok, obviously I'm saying the same thing as matricked, but this sort of thing is hard to wrap my mind around so I think it's nice to hear two people explain it.

Answer 9

we have 4 groups
similiary in the group
AAU, bcs
therefore
4!*3!/2!
4! because of the 4 groups you arrrange
3!/2! because of AAU , an then dividing by 2 as 2as..

Answer 10

Oh I see. Thanks @Kainui @dan815 & @matricked

Answer 11

its nicer to hear 3 people cough

Answer 12

but its best to hear from me okay:) thanks bye

Answer 13

kainui ♥

Answer 14

lol ♥

Answer 15

@Jesstho.-. welcome