How many possibilities are there for the 3?

[Jennifer1990]

Homework Statement

Six digits from the numbers 2, 3, 4, 5, 6, 7, 8 are chosen and arranged in a row without replacement. Find the probability that the digits 2 and 3 appear in the proper order but not consecutively

Homework Equations

The Attempt at a Solution

i know that the denominator is 7!, however I'm having trouble finding the numerator. I think that the numerator is 5C4 * 1 *1 however the answer is 5/21

 

[CompuChip]

Suppose that 2 is in the 1st place. How many possibilities are there for the 3?
If 2 is in the 2nd place, in how many places can you put 3?
And if 2 is in the 3rd position?
etc.

 

[JCVD]

i believe the answer is actually 5/14

 

[CompuChip]

I got something else than 5/21 as well (5/14 sounds familiar). But we will know as soon as Jennifer posts again.

Perhaps she has misquoted the answer, or didn't state the complete question.