TU Wien:Statistik und Wahrscheinlichkeitstheorie UE (Bura)/Übungen 2020W/HW01.2

Symphony orchestra program

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.

(a) How many different programs can it play?

(b) How many different programs are there if the three pieces can be played in any order?

(c) 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?

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Lösungsvorschlag von tabaluga34

--tabaluga34 15:07, 26. Dez. 2020 (CEST)

Symphony orchestra program

a) H*M*B = $30\cdot 15\cdot 9=4050$

b) Permutation of 3 pieces: $30\cdot 15\cdot 9\cdot 3!=24300$

c) ${\binom {54}{3}}={\frac {54!}{3!\cdot (54-3)!}}=24804$