Hi

my question is From a group of 12 children, two random samples of size three are chosen; the first sample being replaced before the second sample is chosen.

a) Four of the group are named Matthew, Mark, Luke and John. Calculate the probability that none of these boys appear in the first sample.

[6 marks]

b) Calculate the probability that the samples have at least one person in common.

[9 marks]

for part a) i know that Number of ways of choosing a sample of 3 is $\displaystyle \dbinom{12}{3}=220$

but i am not sure what to do next and i don't know how to do part b)

thanks