Question

A school director must randomly select 6 teachers to participate in a training session. There are 34 teachers at the school. In how many different ways can these teachers be selected, if the order of selection does not matter?

Answer 1

The formula for the number of combinations when choosing "r" objects (or people) from a larger set of "n" objects (or people) is:
combinations = n! / [r! * (n-r)!]
combinations = 34! / [6! * 28!]
combinations = 34*33*32*31*30*29*28! / [6! * 28!]
combinations = 34*33*32*31*30*29 / 6*5*4*3*2
combinations = 34*33*32*31*29 / 4*3*2
combinations = 34*11*4*31*29
combinations = 1,344,904

Source:
http://www.1728.org/combinat.htm