Question

University needs to send a soccer team to represent the University at a tournament. Assume that the soccer roster has n athletes.

if the soccer squad must also have a captain (selected from the k athletes), how many different ”captained” squads are there? (selecting the same set of players but assigning a different captain counts as different ”captained” squads.)

If every member of the team is to be assigned a jersey (numbers range from 1 to k), how many different ways are there of sending a ”jerseyed” squad?

Answer 1

We can select a team of k athletes from n in ways

To select a captain from these k athletes , we can do this in ways

So total number of captained squads is

Now assuming we have a team of k athletes which have to be numbered, we can the team in ways

And to jersey number 1 we can allot a player in k ways, to jersey number 2 we can allot a player in (k-1) ways and so on

So total ways to allot the jerseys to players is meaning total number of ways is is the total number of jerseyed squads

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