Answer:
[tex]\frac{1}{524160} or 1.910^{-6}[/tex]
Step-by-step explanation:
In order to solve this, you would need to multiply the probability of you choosing the one that goes first, so 1 in 16 discs, then the next one so 1 in 15, and so on untill the fifth disc.
So you would have to do this:
[tex](\frac{1}{16})(\frac{1}{15})(\frac{1}{14})(\frac{1}{13})(\frac{1}{12})\\\frac{1}{524160}[/tex]
That is the probability that the rack ends up in alphabetical order, if you pull discs randomly, 1 in 524160 chances.
Probabilities are used to determine the chances of an event.
The probability that the rack ends up in alphabetical order is [tex]\mathbf{ \frac{1}{524160}}[/tex]
The given parameters are:
[tex]\mathbf{CD = 16}[/tex]
[tex]\mathbf{r = 5}[/tex] -- CDs to arrange
So, the total number of arrangements of 5 CDs from the 16, is:
[tex]\mathbf{Total = ^{16}P_5}[/tex]
Apply permutation formula
[tex]\mathbf{Total = \frac{16!}{(16 - 5)!}}[/tex]
This gives
[tex]\mathbf{Total = \frac{16!}{11!}}[/tex]
Expand
[tex]\mathbf{Total = \frac{16 \times 15 \times 14 \times 13 \times 12 \times 11!}{11!}}[/tex]
[tex]\mathbf{Total = 16 \times 15 \times 14 \times 13 \times 12 }[/tex]
[tex]\mathbf{Total = 524160}[/tex]
There is only one possibility of the CDs being in alphabetical order.
So, the probability is:
[tex]\mathbf{Pr = \frac{1}{524160}}[/tex]
Hence, the probability that the rack ends up in alphabetical order is [tex]\mathbf{ \frac{1}{524160}}[/tex]
Read more about probabilities at:
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