Problem C. 954. (September 2008)

C. 954. Peter's favourite CD has eleven songs on it. He likes the eighth one best. When he inserts the CD in the player, he presses a button to start the first song and then he needs to press another button seven times to reach the favourite song. If he sets the player to ``random'', the player shuffles the 11 songs and plays them in that random order. What is the probability that it takes fewer presses of buttons to reach the favourite song in this way?

Suggested by Á. Számadó

(5 pont)

Deadline expired on October 15, 2008.

Sorry, the solution is available only in Hungarian. Google translation

Megoldás. Összesen 11! a sorba rendezések száma. A kedvenc dal az összekeverés után az első 7 hely valamelyikén lehet. Mind a 7 esetben a többi szám lehetséges sorrendje 10!. Vagyis a valószínűség: $\frac{7\cdot10!}{11!}=\frac{7}{11}$ .

Statistics:

473 students sent a solution.

5 points: 345 students.

4 points: 8 students.

3 points: 8 students.

2 points: 7 students.

1 point: 9 students.

0 point: 90 students.

Unfair, not evaluated: 6 solutionss.

Problems in Mathematics of KöMaL, September 2008

473 students sent a solution.
5 points:	345 students.
4 points:	8 students.
3 points:	8 students.
2 points:	7 students.
1 point:	9 students.
0 point:	90 students.
Unfair, not evaluated:	6 solutionss.

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