Question

A teacher has 12 exams to grade: 8 today and 4 tomorrow. The teacher makes a stack of exams to grade today. How many different combinations of exams to be graded today can be made?

Answer 1

495

Explanation:

This is a combinations question - we don't care in what order the teacher will grade the exam, only that each there are different groupings (much like we don't care about the order in which cards are dealt in a poker game - we only care about the hand we have).

Combination use the general formula:

`C_(n,k)=(n!)/((k!)(n-k)!)` with `n="population", k="picks"`

`C_(12,8)=(12!)/((8!)(4!))`

`C_(12,8)=(12xx11xx10xx9xx8!)/((8!)(4xx3xx2))=11xx5xx9=495`