Question 1160638
<br>
The names are NOT all different....<br>
On the other hand, the statement of the problem is unclear as to whether we can choose, among our 5 names, James and/or John twice -- once from each list.<br>
So perhaps 20C5 is the right answer....<br>
If we can't pick a name twice that is in both lists, then there are 18 different names to choose from, so the number of ways to make the choices would be 18C5.<br>
The problem is a very simple straightforward application of the basic concept of "n choose r".<br>
It's unfortunate that the problem wasn't stated as simply (clearly)....<br>