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(Created page with "<div class="d-none"><math> \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}</math></div> A symphony orchestra has in its repertoire 30 Haydn symphonies, 15 modern works, and 9 Beethoven symphonies. Its program always consists of a Haydn symphony followed by a modern work, and then a Beethoven symphony. <ul><li> How many different pro...") |
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A symphony orchestra has in its repertoire 30 Haydn symphonies, 15 modern works, and 9 Beethoven symphonies. Its program always consists | |||
symphonies, 15 modern works, and 9 Beethoven symphonies. Its program always consists | |||
of a Haydn symphony followed by a modern work, and then a Beethoven symphony. | of a Haydn symphony followed by a modern work, and then a Beethoven symphony. | ||
<ul><li> How many different programs can it play? | <ul style="list-style-type:lower-alpha"><li> How many different programs can it play? | ||
</li> | </li> | ||
<li> How many different programs are there if the three pieces can be played in | <li> How many different programs are there if the three pieces can be played in | ||
Latest revision as of 22:44, 12 June 2024
A symphony orchestra has in its repertoire 30 Haydn symphonies, 15 modern works, and 9 Beethoven symphonies. Its program always consists of a Haydn symphony followed by a modern work, and then a Beethoven symphony.
- How many different programs can it play?
- How many different programs are there if the three pieces can be played in any order?
- How many different three-piece programs are there if more than one piece from the same category can be played and they can be played in any order?