A composer is writing a melody using the twelve-tone technique

Question

A composer is writing a melody using the twelve-tone technique of musical composition. In the twelve-tone technique, each of the twelve tones of the musical scale must be used before any of the tones are repeated. In the composer's melody, no two tones will be used simultaneously. The composer has already chosen the first 8 tones of his melody following this technique.

Based on the information provided, and assuming the composer uses the technique described, select for  Ways to order 4 tones  the number of ways the composer can order the remaining 4 tones of his melody, and select for  Ways to order 3 tones  the number of ways, once the composer has chosen the ninth tone of his melody, the composer can order the remaining 3 tones of his melody. Make only two selections, one in each column.

chetan2u · Answer

You should be able to scan the para and realize that the question is simlar to 12 people to be seated.

1. Eight people have been made to sit and remaining four are to be arranged in four chairs.
First chair: any of four
Second chair: any of the remaining three
Third chair: any of the remaining two
 SO, 4*3*2*1 = 24

2. Nine people have been made to sit and remaining three are to be arranged in four chairs.
First chair: any of three
Second chair: any of the remaining two
Third chair: the last one
 SO, 3*2*1 = 6

Bismuth83 · Answer

1. Choosing 4 notes is the same as choosing A, B, C, and D.

2. Note that order does matter. For example, choosing BACD is different than choosing CADB.

3. So, the number of way to choose 4 notes is the same as the permutation of 4, or  P_4 = 4! = 4 * 3 * 2 * 1 = 24 .

4. The same goes for choosing 3 notes:  P_3 = 3! = 3 * 2 * 1 = 6 .

5. Our answer will be:   Ways to order 4 tones - 24 and Ways to order 3 tones - 6  .

Dbrunik · Answer

Deceptively easy question. Just 4! and 3!.

You don't need to worry about any restrictions simply because you have to use all 12. The restriction here on consecutive tones is totally irrelevant.

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

A composer is writing a melody using the twelve-tone technique

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Two-part Analysis (TPA) Questions

A composer is writing a melody using the twelve-tone technique

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards