There are 52 white keys on a piano. The lowest key is A. The keys are designated A, B, C, D, E, F, and G in succession, and then the sequence of letters repeats, ending with a C for the highest key.

a) If five notes are played simultaneously, in how many ways could the notes all be
i)A's? ii)G's? iii)the same letter? iv)different letters?
b) If five keys are played in order, how would your answer in part a) change?

How do you do iv from part a and part b for iv?

Check Steve's solution for the same question.

http://www.jiskha.com/display.cgi?id=1436351642

I suggest that you scroll down on this page and you will see the same question. Other people have already answered this.

I already saw this post and he didn't help with part IV with different letters. That's the part I'm having trouble on...

To solve part iv of both questions, you need to consider the concept of combinations. A combination is a selection of items from a larger set without regard to the order of the items.

a) To calculate the number of ways in which the notes can have different letters, you can use combinations. Since there are 7 different letters (A, B, C, D, E, F, G), you can choose any 5 of them for the notes. The formula for combinations is nCr, where n is the total number of items and r is the number of items chosen. The number of ways for different letters would be calculated as 7C5.

b) If five keys are played in order, the answer to part a) changes as we now need to consider the order of the chosen keys. We need to use permutations instead of combinations. A permutation is an arrangement of items from a larger set taking into account the order of the items.

To calculate the number of ways in which the keys can have different letters and be played in order, you need to use permutations. The number of ways can be calculated using the formula nPr, where n is the total number of items and r is the number of items chosen in a specific order. The number of ways for different letters in order would be calculated as 7P5.

So, in both part a) and b) for iv), you would use combinations for part a and permutations for part b to calculate the number of ways for different letters.