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