For the abba question, what did people do? I think I put the wrong numbers into the calculator, but my method was:
3/7 * 2/6 * 2/5 * 1/4 (picking the letters AABB).
There are 6 ways to arrange AABB, so multiply by 1/6. This gets 1/420. I think then multiply by 4! as it does not matter what order we pick the cards from the initial 7.