Snoopy Services is taking care of 15 dogs. Six of the dogs are large, while the remaining nine dogs are small. The manager would like to take the dogs out for walks in groups of five, each with a different handler.

a) How many ways can the 15 dogs be walked in groups of five?

b) How many ways can the 15 dogs be walked in groups of five, if there must be exactly two large and three small dogs per group?