how many ways can a group of 3 students be chosen from a class of 30?

Question

anonymous · Answer

There are 30 possibilties for the first, 29 for the second, and 28 for the third, for a total of 30*29*28.  However, you don't really care what order you chose the students, and so a choice of Sue, Ellen and Buffalo Bill in that order is actually the same, so far as you're concerned, as the choice of Ellen, Bill and Sue in that order.  How many such "duplications" are there?  The number of ways of re-arranging a group of three students, which is 3x2 = 6.  So your first calculation has 6 duplicates for each "real" choice.  To fix this, divide by 6.  So your final answer is 30*29*28/6 = 4060.