A pilot and a copilot are to be chosen from a group of five pilots. How many different crews are possible?

Question

a pilot and copilot are to be chosen from a group of five Pilots. how mant different crews are possible 

Answer 1

It depends what is meant by "different".

 

Is a crew with pilot A and copilot B considered different from a crew with pilot B and copilot A?  I would think the answer is yes.

 

If that's the case, then:

 

There are 5 different choices for pilot.  Once a pilot is chosen, there are 4 possible choices for copilot.  Therefore there are 20 different crews.

 

Or you can use the rule for permutations.  The number of permutations of k items chosen out of a set of n items is n!/(n-k)!.  In this case, that gives 5! / 3! = 5*4 = 20.

 

HOWEVER, if all they care about is who is in the crew and NOT which person has which role, then you have to use the rule for combinations:

 

n! / (n! (n-k)!)

 

That gives 5! / (3! * 2!) = 10.