Anne has to pick 20 questions to do on a test. There are 23 questions total. How many different groups groups of 20 are there?

Question

This is a very difficult problem that I could not understand.  If you can figure it out, I would be very happy.  Thx

Answer 1

This is a combinations problem which is different from permutations.

So the formula for combinations is

nCr= n!/((n-r)!r!)

 

n= The total number of questions 23

r= The group of 20

 

23!/(23-20)!20!

 

=23!/3!20!

 

=23x22x21/3!

 

=1771 different ways to pick 20 problems out of 23

Answer 2

There are 23C20 ways to pick questions on the test (read as 23 choose 20).  This represents the various ways that the 20 can be picked without respect to order.  There are 23! total ways and 20! ways to arrange 20 items and there's 3! ways to arrange the remaining 3 questions.  

 

This gives us 23C20 = 23!/20!/3! = 1771 ways.