Question

You own 24 CDs. You want to randomly arrange 7 of them in a CD rack. What is the probability that the rack ends up in alphabetical order

Answer 1

Answer:

the probability that the rack ends up in alphabetical order is 0.0001984

Step-by-step explanation:

Given that:

You own 24 CDs. You want to randomly arrange 7 of them in a CD rack.

Th probability that the rack ends up in alphabetical order can be determined by taking note of the permutations and combinations.

From above; all possible permutations of size 7 we can derive from 24 is

24P7

Similarly,we are meant  to estimate  all the possible ways a unique set of 7 things can be gotten from a total of 24

i.e

24 C7

∴

The probability = $\dfrac{^{24}{C}_7}{^{24}{P}_7}$

= $\dfrac{\dfrac{24!}{7!(24-7)!} }{ \dfrac{24!}{(24-7)!} }$

=$\dfrac{\dfrac{24!}{7!(17)!} }{ \dfrac{24!}{(17)!} }$

= $\dfrac{346104}{ 1.74436416 \times 10^9}$

= 0.0001984

the probability that the rack ends up in alphabetical order is 0.0001984

Answer 2

The probability that the rack ends up in alphabetical order is 0.0001984

The total number of CD is given as:

$\mathbf{n = 24}$

The number of CDs to select is given as:

$\mathbf{r = 7}$

The number of arrangement of 7CDs in 24 is represented as 24P7

So, we have:

$\mathbf{^{24}P_7 = \frac{24!}{(24 - 7)!}}$

$\mathbf{^{24}P_7 = \frac{24!}{17!}}$

Simplify

$\mathbf{^{24}P_7 =1744364160}$

The number of selecting 7 CDs from 24 is represented as 24C7

So, we have:

$\mathbf{^{24}C_7 = \frac{24!}{(24 - 7)!7!}}$

$\mathbf{^{24}C_7 = \frac{24!}{17!!7}}$

Simplify

$\mathbf{^{24}C_7 =346104}$

So, the probability is:

$\mathbf{Pr = \frac{346104}{1744364160}}$

Divide

$\mathbf{Pr = 0.0001984}$

Read more about permutation and probability at:

https://brainly.com/question/14767366