2008 NYJC P2 Q6

Five girls Mary, June, April, Alice and Deborah, and five boys Matthew, Mark, Luke, John and Paul, stand in a queue in random order to enter the ballroom for Dinner and Dance 2008 – Splendour. Find the probability that

1. Matthew is first and Mary is sixth in the queue,[1]
2. either Alice is first or Mark is second (or both) in the queue,[2]
3. there is only one girl chosen if five people are chosen at random from this group,[2]
4. all five girls are next to each other given that at least four boys stand next to each other.[3]