Coach Miller is filling out the starting lineup for his indoor
soccer team. There are 10 boys on the team, and he must
assign 6 starters to the following positions: 1 goalkeeper, 2 on
defense, 2 in midfield, and 1 forward. Only 2 of the boys can
play goalkeeper, and they cannot play any other positions. The
other boys can each play any of the other positions. How many
different groupings are possible?
Let us make hay while the sun shines.
Don Quixote. Part i. Book. iii. Chap. xi.