The teacher of a senior class needs to choose 4 members of the class to represent the school. if there are 10 seniors in the class, how many different ways are there for the teacher to choose 4 in no particular order?

There are 10 seniors in the class, from which 4 should be chosen by the teacher. The order of the chosen students does not matter. This means that we speak of combinations. THe equation for calculating the number of possible combinations is:
C=N!/R!(N-R), where N is the total number of objects and R is the number of objects we select from the N 
In our case, N=10, R=4.
C= 10!/4!*6!=10*9*8*7*6!/6!*4*3*2*1=10*9*8*7/24=5040/24=210
There are 210 different ways for the teacher to choose 4 seniors in no particular order.