Students AB and C compete in a series of tests For coming in

Students A,B and C compete in a series of tests. For coming in first on any given test, one is awarded x points; for placing second, y points; and for third place, z points. Let x, y, and z be natural numbers with x > y > z. Assume no ties on any of the tests. Student A accumulated 20 points; student B got 10 points, and student C got 9 points. Student A came in second on the Algebra test. Who finished second on the Geometry test? What is the point allocation for 1st, 2nd and 3rd place?

Solution

Here having filled it, there are 3 things left and anyone of these 3 things can be used to fill first place. So the first place can be filled in 3 ways.

and

again have to fill it, there are 2 things left and anyone of these 2 things can be used to fill second place. So the second place can be filled in 2 ways.

remain 3 rd, there are only 1 things left and anyone of this one things can be used to fill last place. So the 3rd place can be filled in 1 ways.

Hence by fundamental principal of multiplication, the 1st, 2nd and 3rd places can be filled in 3 X 2 X 1 ways

So the total number of arrangements will be 3 X 2 X 1.