Question

How many permutations of the letters A to H if the three letters ABC has to occur consecutively?

What if they must appear together, but not necessarily consecutively?

Answer 1

what do you mean appear together but not necessarily consecutive?

Answer 2

did you mean the permutation of ABC are the considered the same?

Answer 3

I think the question has 2 part.

1 part is ABC consecutive.

2nd part is ABC or BCA or CBA that sort

Answer 4

1) 6!
2) 3! 6!

Answer 5

Ah thanks. I feel bad now.

Answer 6

wait again y 6!?

A-H is 8 characters.

Answer 7

(ABC) _ _ _ _ _

there are 8 letters. When you move ABC together, that is considered one object. And you permute it with the other 5 letters.

Answer 8

So isn't it 5! instead

Answer 9

no it's 6. ABC is consider one object, together with the other 5 letters, make 6 distinct objects.

Answer 10

(ABC) (D) (E) (F) (G) (H). see? 6 of them

Answer 11

Ah I see!

Answer 12

then the 3! for part is is for the permutation of ABC

Answer 13

correct