Hello, SyNtHeSiS!

You can "talk" your way through these . . .

A Quidditch team consists of seven players: .

a) The Puddlemere United club has 32 active players.

Assuming that every Puddlemere player can play in any position,

how many different teams can the club field?

From the 32 players, choose 3 Chasers: . ways.

From the remaining 29 players, choose 2 Beaters: . ways.

From the remaining 27 players, choose 1 Keeper: . ways.

From the remaining 26 players, choose 1 Seeker: . ways.

Therefore, there are: . possible teams.

Basically, it's the same procedure.b) The Chudley Cannons have 23 players under contract.

Three of these players specialise at playing as Keepers, while 8 prefer to be Beaters.

The remaining 12 players are happy to play either as Chasers or Seekers.

How many different teams can the Chudley Cannons form?

From the 3 available Keepers, choose 1: . ways.

From the available 8 Beaters, choose 2: . ways.

From the remaining 12 players, choose 3 Chasers: . ways.

From the remaining 9 players, choose 1 Seeker: . ways.

Therefore, there are: . possible teams.