How many ways can we select a group of 4 people from a class of 27? Please explain
How many ways can we select a committee of 2 people from a staff of 5?
The first member of the committee can be chosen from 5 people, and the second can be chosen from 4. So the number of possible choices is 5*4=5!/(5-2)!
However, the 2 people could have been chosen in the order A then B, or B then A, in 2! ways. We have to reduce the above choices by this factor, which gives the answer as 5!/((5-2)!2!) ways.
In short, this is represented by C(5,2) or simply (5,2) ways.
So, in general, to choose a group of k people from a class of n can be done in
C(n,k) ways, or n!/((n-k)!k!) ways.