Question 629274
<pre>
The answer would be 4! or 24 ways if it didn't matter whether 3 and 4
were side by side or not.  From the 4! we must subtract the ways in which
 they are side by side.  There are 2 cases where they can be side by side:

Case 1. When the 3 is left of the 4, which means we are arranging these three
things:  1, 2, 34 which is 3! or 6 ways.

Case 2. When the 4 is left of the 3, which means we are arranging these three
things:   1, 2, 43 which is also 3! or 6 ways.

So the answer is 4! - 2×3! = 24 - 2×6 = 24 - 12 ways.

But, heck, by the time you did all that you could just have listed them all
and counted them:

 1. 1324
 2. 1423
 3. 2314
 4. 2413
 5. 3124
 6. 3142
 7. 3214
 8. 3241
 9. 4123
10. 4132
11. 4213
12. 4231

Edwin</pre>