A certain professional soccer team runs a 4-4-2 formation on the field. This means they play with 4 defenders, 4 midfielders, 2 forwards, and 1 goalkeeper on the field. If the team has 6 defenders, 5 midfielders, 3 forwards, and 2 goalkeepers, how many different groups of 11 starting players could they have?

Question

A certain professional soccer team runs a 4-4-2 formation on the field. This means they play with 4 defenders, 4 midfielders, 2 forwards, and 1 goalkeeper on the field. If the team has 6 defenders, 5 midfielders, 3 forwards, and 2 goalkeepers, how many different groups of 11 starting players could they have? 
note that:Each player only plays in his designated position. The 2nd goalkeeper is not allowed to play as a defender.

Steve · Answer

just find out how many possibilities there are for each position, and multiply them all together:

C(6,4) * C(5,4) * C(3,2) * C(2,1) = 450

If your comment about the 2nd goalkeeper means that he may play as a midfielder or a forward, then things get more complicated.

amgad ahmed · Answer

ur answer is totally correct....thank u very much