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June 2005 p6 q7
2879
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:
if the captain, who is a midfield player, must be included, together with one defence and one forward player,
if exactly one forward player must be included, together with any two others.
Solution
(i) Since the captain, a midfield player, must be included, we need to choose 1 player from the 3 defence players and 1 player from the 5 forward players. The number of ways to do this is given by:
(ii) If exactly one forward player must be included, we choose 1 player from the 5 forward players. Then, we choose 2 more players from the remaining 6 players (3 defence and 3 midfield). The number of ways to do this is given by: