A competition has a first prize, a second prize, a third prize and a fourth prize. Ten competitors enter this competition and the prizes are awarded for the first, second, third and fourth competitors. in order of merit.

(a) Find the number of different ways in which these prizes could be won. Smith and Jones are two of the ten competitors. Find the number of different ways in which the prizes could be won if

(b) neither Smith nor Jones wins a prize,

(c) each of Smith and Jones wins a prize.