You used cases in some of the permutation calculations in Lesson 2. You would add the number of permutations in each case to determine the total. There are also some combination questions that require the use of cases.

 

Pianists can create different chords by pressing several keys down at the same time on a piano.

 

Think about how many chords are possible in each of the following situations.

 

• Using the keys from the piano as shown, how many different chords—combinations of two or more keys—can be produced using exactly four fingers if each finger only presses one key, black or white, at a time?
• How many chords can be produced using three or four fingers?
• How many chords can be produced using two or three or four fingers?

Watch Piano Chords to see how the number of chords can be calculated for each situation.