DATA ANALYSIS AND PROBABILITY are common core content. Common core content means it touches K-12 students.

The State expected 8th grade student to master how to solve counting problem and to master how to use factorial to solve combination problem. Learning how to compute factorial is needed in permutation and combination analysis.

Performance Objective:

After this tutorial the students are expected to solve counting problems and represent counting principle algebraically including factorial notation. The above problem is a combination problem.

To learn how to count the possible combination . You must remember you only count the distinct combination.
For example the combination ( book1, book2, book3 ) is one (1) count the combination (book2, book1,book3) is not distinct or different from the above combination so it is not counted. Furthermore the combination (book3,book1,book2) is not different or distinct from the above combination so it is also not counted.
Now let us do the manual counting of the possible combination to solve the above problem.

Using the above table there are only 20 possible distinct combination or 20 possible ways to select 3 books out of the six books.

Using Excel spreadsheet, you solve the problem using the formula COMBIN. You will get the same result, which is 20.

Another mathematical tool is using the combination formula and knowledge about factorial.