Aschool 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?

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

The household makes $424.45