A football team consists of 3 players who play in a defence position,

3 players who play in a midfield position and 5 players who play in a

forward position. Three players are chosen to collect a gold medal for the

team. Find in how many ways this can be done

(a) if the captain, who is a midfield player, must be included, together

with one defence and one forward player.

(b) if exactly one forward player must be included, together with any two

others.

(ii) Find how many different arrangements there are of the nine letters in the

words GOLD MEDAL

(a) if there are no restrictions on the order of the letters,

(b) if the two letters D come first and the two letters L come last.