Problem Solving

So I was doing a test online from 800score.com and I got this question:

1,2,3,4,5 are given
If you can use each number from above only once, how many ways can the 5 digits above be arranged such that 4&5 are not adjacent?

Can someone please give me a formula i can use for this? Or a source where I can check it.

Thank you!
De Jan

total possibilities: 5!
Undesired permutations = 48
45--- = 6 possibilities
-45-- = 6 possibilities
--45- = 6 possibilities
---45 = 6 possibilities
54--- = 6 possibilities
-54-- = 6 possibilities
--54- = 6 possibilities
---54 = 6 possibilities

5! - 48 = 72 is the answer

total possibilities: 5!

possibility in which both 4 and 5 are together = 4! *2

so probability of 4 and 5 always together = 4! *2/5!

so Prob of 4 and 5 never together = 1- 4!*2/5!

= 3/5 = 0.6


Hope this helps

Karan