Question

A school gives 6 different subject awards (math, history, English, etc.) to a graduating class of 82 students. No student can win more than one award. How many outcomes are possible? Just set up the problem.

Answer 1

Here we will take 2 cases.

1) only 6 awards to be distributed amongst 82 students.

2) every student will an award.

case I :

if only 6 awards are to be distrubuted amongst 82 students. then it is a combination problem.

accordingly we need to choose 6 students amongst 82 graduating students.

so we represent the equation by combination as , so the possible combinations are

C(n,r)= C(82,6)

=

=350161812

therefore there are 350161812 no of possibilities

Case 2 :

if every student is supposed to receive an award then each student will receive an award out of the 6 subjects.

so there are 6 combinations for each student to receive an award.

so as there are 82 students the total no of combinations will be 6 X 6 X 6 X .........82 times .

simply put as, .

therefore total number of combinations will be .