Question

In how many different ways can a committee of 4 students be chosen from 6 students

Answer 1

If order mattered, then there would be 6*5*4*3 = 30*12 = 360 different ways to form the committee. However, no single member outranks the other. Each member has equal ranking. So order does not matter. 

Since order does not matter, we must consider all of the ways to arrange a single group of 4 people. That is 4! = 4*3*2*1 = 24 ways. We overcount by a factor of 24 when order doesn't matter which is why we divide the previous result (360) by 24 to get 360/24 = 15

Answer: 15

Note: you can use the combination formula n C r = (n!)/(r!*(n-r)!) with n = 6 and r = 4 to get the same answer