Question

1) Berizon Virefull is looking for a new jingle. Due to the attention span and vocal range of their target audience, they are looking for a 4 note jingle contained within an octave (C0-C1). Thus pick 4 notes from 13. Repeated notes are allowed and order does matter. How many possible jingles are there?

2) Considering that some of the submittions (see above problem) were boring, Berizon now insists that no note can be repeated, but order still matters. How many possible jingles are there now?

3) If order did not matter, and repetitions were not allowed, how many jingles?

4) If order does not matter and repetitions are allowed?

Answer 1

1.Since there are 13 notes to choose from, the number of possible jingles with repeated notes and order matters is given by the formula for permutations with repetition: 13^4 = 28,561.

2.If no note can be repeated, then we need to use the formula for permutations without repetition: P(13, 4) = 13 x 12 x 11 x 10 = 17,160.

3.If order does not matter and repetitions are not allowed, we need to use the formula for combinations: C(13, 4) = (13!)/(4!(13-4)!) = 715.

4.If order does not matter and repetitions are allowed, we need to use the formula for combinations with repetition: C(13+4-1, 4) = C(16, 4) = (16!)/(4!(16-4)!) = 1820.