a.) a man and a woman will be selected to demonstrate the latest dance step. How many choices are there for this selection assuming they all know the dance step?

b.) After the demonstration, each man will be paired with a woman (each woman will be paired with one man) and they will all dance this latest step. How many different ways can these dance pairings be made?

c.) After the dance two people will be selected to show the slides from the last dance party. How many different assignments are possible for this task?

for each question, here is what i think:

a.) ten choices for men and 10 choices for women 10*10 = 100 choices

b.) 10! possibilities

c.) 20C2 = 190 possibilities

am i thinking correctly on this question?