There are 24 ways to choose the activities of these three people at different times: c12c13c14 =,
The probability of these three people participating in different activities is p=24C39=27.
(2) From the meaning of the question, ξ = 2, 3, 4, 5, 6,
P(ξ=2)=C22C29= 136，
p(ξ= 3)= c 12c 13c 29 = 16，
p(ξ= 4)= C23+c 12c 14c 29 = 1 136，
p(ξ= 5)= c 13c 14c 29 = 13，
P(ξ=6)=C24C29= 16。
The list of ∴ξdistribution is:
? ξ? 2? 3? 4? 5? 6? p？ 136? 16? 1 136? 13? 16eξ= 2× 136+3× 16+4× 136+5× 13+6× 16 = 409。