Question

You own 24 CDs. You want to randomly arrange 9 of them in a CD rack. What is the probability that the rack ends up in alphabetical order? The probability that the CDs are in alphabetical order is

278

likes
1389 views

Answer to a math question You own 24 CDs. You want to randomly arrange 9 of them in a CD rack. What is the probability that the rack ends up in alphabetical order? The probability that the CDs are in alphabetical order is

Expert avatar
Sigrid
4.5
116 Answers
1. Calculate the total number of ways to arrange 9 CDs out of 24. This is the number of permutations of 9 CDs, given by:

24P9 = \frac{24!}{(24-9)!} = \frac{24!}{15!}

2. For the arrangement to be in alphabetical order, there is exactly 1 way (since only one specific order is alphabetical).

3. The probability that the CDs are in alphabetical order is the number of favorable outcomes (1) divided by the total number of arrangements calculated in step 1:

\frac{1}{\frac{24!}{15!}} = \frac{15!}{24!}

4. Simplify this to get the probability that the CDs are in alphabetical order:

\frac{1}{9!}

Therefore, the final answer is: \frac{1}{9!}=\frac{1}{362880}

Frequently asked questions (FAQs)
What is the value of 3 multiplied by 8, added to 10 divided by 2, minus 5?
+
What is the probability of getting at least 2 heads when flipping 5 fair coins?
+
What is the domain and range of y = ∛(x + 4) - 2?
+
New questions in Mathematics
Let X be a discrete random variable with range {1, 3, 5} and whose probability function is f(x) = P(X = x). If it is known that P(X = 1) = 0.1 and P(X = 3) = 0.3. What is the value of P(X = 5)?
5 people can complete a task in 72 hours. How many people are needed to complete the task in 60 hours.
Determine the equations of the lines that pass through the following points P1 (2;-1) and p2 (4;-1)
[(36,000,000)(0.000003)^2]divided(0.00000006)
You are planning to buy a car worth $20,000. Which of the two deals described below would you choose, both with a 48-month term? (NB: estimate the monthly payment of each offer). i) the dealer offers to take 10% off the price, then lend you the balance at an annual percentage rate (APR) of 9%, monthly compounding. ii) the dealer offers to lend you $20,000 (i.e., no discount) at an APR of 3%, monthly compounding.
Mrs. Emily saved RM10000 in a bank. At the end of the eighth year, the amount of money accumulated amounted to RM19992.71. If the bank pays an annual interest of x% for a year compounded every 6 months. Calculate the value of x.
Substitute a=2 and b=-3 and c=-4 to evaluate 2ac/(-2b^2-a)
Find all real numbers x that satisfy the equation \sqrt{x^2-2}=\sqrt{3-x}
19) If the temperature of -8°C decreases by 12°C, how much will it be? a)-20°C -4°C c) 4°C d) 20°C
Determine the Linear function whose graph passes through the points (6, -2) and has slope 3.
Calculate the change in internal energy of a gas that receives 16000 J of heat at constant pressure (1.3 atm) expanding from 0.100 m3 to 0.200 m3. Question 1Answer to. 7050J b. 2125J c. None of the above d. 2828J and. 10295 J
nI Exercises 65-68, the latitudes of a pair of cities are given. Assume that one city si directly south of the other and that the earth is a perfect sphere of radius 4000 miles. Use the arc length formula in terms of degrees to find the distance between the two cities. 65. The North Pole: latitude 90° north Springfield, Illinois: latitude 40° north
2.3 X 0.8
How much does 7.2 moles of ammonium dichromate weigh? (NH4)2Cr2O7
Arturo had hospitalization expenses of $8,300. Your policy for medical expenses Seniors have a deductible of $500 and expenses are paid at a 20% coinsurance. These are the first expenses ever this year, how much will Arturo have to pay in your bill for hospitalization expenses?
Recall that with base- ten blocks, 1 long = 10 units, 1flat = 10 long, and a block = 1 unit. Then what number does 5 flat, 17long and 5 units represent represent ?
y’’ -4y’ +4y = (12x^2 -6x)e^2x Y(0)= 1 Y’(0)=0 Y(x)=c1y1+c2y2+yp
Two trains leave stations 294 miles apart at the same time and travel toward each other. One train travels at 95 miles per hour while the other travels at 115 miles per hourHow long will it take for the two trains to meet?
I have a complex function I would like to integrate over. I can use two approaches and they should give the same solution. If I want to find the contour integral ∫𝛾𝑧¯𝑑𝑧 for where 𝛾 is the circle |𝑧−𝑖|=3 oriented counterclockwise I get the following: ∫2𝜋0𝑖+3𝑒𝑖𝑡⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯𝑑(𝑖+3𝑒𝑖𝑡)=∫2𝜋03𝑖(−𝑖+3𝑒−𝑖𝑡)𝑒𝑖𝑡𝑑𝑡=18𝜋𝑖 If I directly apply the Residue Theorem, I would get ∫𝛾𝑧¯𝑑𝑧=2𝜋𝑖Res(𝑓,𝑧=0)=2𝜋𝑖
Construct a set of six pieces of data with​ mean, median, and midrange of 67 and where no two pieces of data are the same.