There are 4 high schools high schools a high school b high s

There are 4 high schools, high schools a, high school b, high school c, high school d, at the end of season the city is creating a super start team of ten players. THere is no guarantee on how many players from each school will be picked (for example all ten kids from A could be chose or 5 from A 3 from B 2 from C 0 from D, etc) In how many ways could these schools be represented on the all star team. (note: a representation refers to how many players from that school could be chosen, not which individual players: also note that each school has at least 10 players)

Solution

since there are 4 high schools and we need to pick 10 players.

each school has 10 players

so there are total 40 players.

now we need to pick 10 players out of 40 players.

so number of ways is given by

40*39*38*37*36*35*34*33*32*31