If a CD player is programmed to play the CD tracks in random order and there are six songs on your CD, what is the probability that it will play the songs in order from your favourite to your least favourite?
If a CD player is programmed to play the CD tracks in random order and there are six songs on your CD, there are a total of 6! (6 factorial) possible orders in which the songs can be played.
Since we want the CD player to play the songs from your favorite to your least favorite, there is only one specific order that satisfies this condition.
Therefore, the probability that the CD player will play the songs in order from your favorite to your least favorite is:
1/(6!) = 1/720 ≈ 0.00139 or 0.139%.
To determine the probability that the CD player will play the songs in order from your favorite to your least favorite, we first need to consider the total number of possible arrangements of the songs. Since there are six songs, there are 6! (read as "6 factorial") ways to arrange them.
6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
Out of these 720 possible arrangements, only one arrangement corresponds to your favorite song playing first, followed by your second-favorite song, and so on, until your least favorite song plays last. So, the probability of this specific arrangement happening is 1 out of 720.
Therefore, the probability that the CD player will play the songs in order from your favorite to your least favorite is 1/720 or approximately 0.0014 (0.14%).