There are 15 players in a junior soccer team. It is needed to select 2 attackers, 3 midfielders, 3 defenders and a goalkeeper to the starting lineup (any player can play any position).
How many possible ways there exist to select the starting lineup? Remember that in addition to the starting lineup there are those player who are not selected to the starting lineup.
My attempt: ${15 \choose 2, 3, 3, 1, 6}\ = 25225200$. Is multinomial coefficient formula the right approach on this one?
This is case of distribution of distinct objects into distinct groups. $$ $$ First select 2 for attacker position then from rest select 3 for mid field and then from rest 3 defender. $$\therefore ={15 \choose 2}{13 \choose 3}{10 \choose 3}$$