Question

In: Statistics and Probability

3. A “chord” (two or more notes played simultaneously, rather than one at a time) consists...

3. A “chord” (two or more notes played simultaneously, rather than one at a time) consists of an unordered selection (without repetition) from among the seven notes {A, B, C, D, E, F, G}.

a. How many different four note “chords” are possible?

b. How many different four note “chords” are there such that “A” is one of the four notes?

c. How many four note “chords” are there such that “A” is NOT one of the four notes?

Expert Solution

A “chord” consists of an unordered selection (without repetition) from among the seven notes {A, B, C, D, E, F, G}.

So there are total 7 notes .

Unordered selection means combination . We select r items from total n items in nCr ways .

And its formula is

a) Four cords are selected in 7C4 ways .

b) How many different four note “chords” are there such that “A” is one of the four notes

So, here A is fixed , So we have to choose 3 notes from 6 notes

We can select 3 notes from 6 notes in 6C3 ways .

c) How many four note “chords” are there such that “A” is NOT one of the four notes?

So, here A is excluded from selection , so, we can select 4 notes from total 6 notes .

We can select 4 notes from 6 notes in 6C4 ways ..

orchestra answered 2 years ago

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