In how many ways can you select a team where there is a captain and an assistant captain

Question

A group of 30 students try out for a soccer team, which consists of 11 players.

Answer 1

// I only see one direct question but I am assuming there is two.

 

First:

A group of 30 students try out for a soccer team, which consists of 11 players.

 

//Combination is used because it does not matter what order the players are in. example students Bob, Jim, Tom is the same as Jim, Tom, Bob

 

Out of the 30 students pick 11.

₃₀C₁₁= 30!/ 11! (30-11)!= 30!/11!(19)!= 54627300

 

Combinations: 54627300

 

Second:

How many ways can you select a team where there is a captain and an assistant captain?

// The questions suggests that we use combination because it asks for how many different way, we can select two positions out of the 11 players.

 Out of the 11 players pick 2 captains

₁₁C₂= 11!/2!(11-2)!= 11!/2!(9)!= 55

Combination: 55

 

// Looks like we might be able to use permutations calculations, depending on what your teacher is looking for because this question may be suggesting an order of rank. For an order you would need a permutations calculator because Jim, Bob, Tom are different from Bob, Jim, Tom.

 

Out of 11 players pick 2 captains.

₁₁P₂= 11!/(11-2)!= 11!/9!= 110

Permutations= 110

 

 

// you can use a scientific calculator to calculate your answers. Usually the "!" is in the top left and remember to follow order of operations.