How many melodies? #1

Probability Level 1

My toy piano keyboard has 7 distinct white notes: letters A-G in English alphabet. I'm going to create a melody by playing three random notes. I can repeat a note for two or three times (six examples are given below). How many different melodies I can play?

Examples:

C D E

A B G

C B C

G E E

A A F

D D D


The answer is 343.

Chrishan Silva by Chrishan Silva , 29, USA

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2 solutions

Chrishan Silva
Aug 30, 2014

As there are seven different notes, I've got 7 choices for the first note I'm playing. Similarly, I've got 7 choices for second and third notes too. From the theory of counting, all possible combinations equal to 7 ∗ 7 ∗ 7 = 343 7*7*7=343 .

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Did the same way..

Manish Mayank - 6 years, 7 months ago

Since there are total a number of 7 letters and we need to make a 3-lettered word with/without meaning, it is a simple case of permutations. The first place of the 3-lettered work can be occupied by 7. The second by 7 and the third by 7 as well...(as repetition is allowed) So, by fundamental theorem of Multiplication, total number of ways = 7x7x7 = 343

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