Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

What is the total number of different 12-letter arrangements that can be formed using the letters in the word ANNUNCIATION? Answer:

What is the total number of different 1212-letter arrangements that can be formed using the letters in the word ANNUNCIATION?\newlineAnswer:

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Grade 7right chevron icon
Convert between customary and metric systemsright chevron icon

Full solution

Q. What is the total number of different 1212-letter arrangements that can be formed using the letters in the word ANNUNCIATION?\newlineAnswer:
  1. Determine Frequency of Each Letter: Determine the frequency of each letter in the word ANNUNCIATION. AA appears 33 times, NN appears 44 times, UU appears 11 time, CC appears 11 time, II appears 11 time, 3300 appears 11 time, and 3322 appears 11 time.
  2. Calculate Total Number of Letters Factorial: Calculate the factorial of the total number of letters.\newlineThe word ANNUNCIATION has 1212 letters, so we calculate 12!12! (1212 factorial).\newline12!=12×11×10×9×8×7×6×5×4×3×2×112! = 12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1
  3. Calculate Factorial of Each Letter Frequency: Calculate the factorial of the frequency of each letter.\newlineA appears 33 times, so we calculate 3!3!.\newline3!=3×2×13! = 3 \times 2 \times 1\newlineN appears 44 times, so we calculate 4!4!.\newline4!=4×3×2×14! = 4 \times 3 \times 2 \times 1\newlineU, C, I, O, and T each appear 11 time, so their factorials are all 1!1!.\newline1!=11! = 1
  4. Use Formula for Permutations: Use the formula for permutations of a multiset to find the total number of different arrangements.\newlineThe formula is:\newlineTotal arrangements =12!3!×4!×1!×1!×1!×1!×1!= \frac{12!}{3! \times 4! \times 1! \times 1! \times 1! \times 1! \times 1!}
  5. Perform Calculations: Perform the calculations.\newlineTotal arrangements = (12×11×10×9×8×7×6×5×4×3×2×1)/((3×2×1)×(4×3×2×1)×1×1×1×1×1)(12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1) / ((3 \times 2 \times 1) \times (4 \times 3 \times 2 \times 1) \times 1 \times 1 \times 1 \times 1 \times 1)\newlineTotal arrangements = (12×11×10×9×8×7×6×5)/(6×24)(12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5) / (6 \times 24)\newlineTotal arrangements = (12×11×10×9×8×7×5)/24(12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 5) / 24\newlineTotal arrangements = (12×11×10×9×8×35)/24(12 \times 11 \times 10 \times 9 \times 8 \times 35) / 24\newlineTotal arrangements = (12×11×10×9×2×35)(12 \times 11 \times 10 \times 9 \times 2 \times 35)\newlineTotal arrangements = (12×11×10×18×35)(12 \times 11 \times 10 \times 18 \times 35)\newlineTotal arrangements = (12×11×180×35)(12 \times 11 \times 180 \times 35)\newlineTotal arrangements = (12×1980×35)(12 \times 1980 \times 35)\newlineTotal arrangements = (12×69300)(12 \times 69300)\newlineTotal arrangements = 831600831600

More problems from Convert between customary and metric systems

Question
Convert: \newline1 1 tbsp 2 2 tsp = _____ \_\_\_\_\_ tsp
Get tutor helpright-arrow

Posted 7 months ago

Question
Omar consumed 710710 milliliters of energy drink yesterday. How many liters of energy drink did he consume?\newline(Round your answer to the nearest hundredth of a liter.)
Get tutor helpright-arrow

Posted 8 months ago

Question
A real estate purveyor purchases a 6060,000000 square foot (ft2) \left(\mathrm{ft}^{2}\right) warehouse and decides to turn it into a storage facility. The warehouse's width is exactly 23 \frac{2}{3} of its length. What is the warehouse's width? Round your answer to the nearest foot.
Get tutor helpright-arrow

Posted 8 months ago

Question
A baker uses 33 cups (c) of flour to bake 22 loaves of bread. If 11 pound (lb) of flour is equivalent to 313c 3 \frac{1}{3} \mathrm{c} , how many loaves of bread can the baker make with a 10lb 10 \mathrm{lb} -bag of flour?\newline(Round the answer to the nearest whole number.)
Get tutor helpright-arrow

Posted 7 months ago

Question
Ella deposited $2500 \$ 2500 into a savings account.\newlineThe relationship between the time, t t , in years, since the account was first opened, and Ella's account balance, B(t) B(t) , in dollars, is modeled by the following function.\newlineB(t)=2500⋅e0.025t B(t)=2500 \cdot e^{0.025 t} \newlineWhat will the balance of Ella's savings account be after 44 years? Round your answer, if necessary, to the nearest hundredth.\newline$ \$
Get tutor helpright-arrow

Posted 8 months ago

Question
Maya needs to rent a car while on vacation. The rental company charges $17.95\$17.95, plus 1818 cents for each mile driven. If Maya only has $40\$40 to spend on the car rental, what is the maximum number of miles she can drive? \newlinemiles \newline(Round your answer down to the nearest whole mile)
Get tutor helpright-arrow

Posted 8 months ago

Question
What is the area of a circle whose circumference is 14471447 meters? (Use π=3.14\pi=3.14 ) (Answer: 166698.73 m2166698.73\,\text{m}^2 )
Get tutor helpright-arrow

Posted 8 months ago

Question
What is the area of a circle whose circumference is 14471447 meters? (Use π=3.14\pi = 3.14) (Answer: 166698.73 m2166698.73 \, \text{m}^2)
Get tutor helpright-arrow

Posted 7 months ago

Question
Convert 1313 feet to meters using 3.2813.281 feet : 11 meter\newlineRound answers to hundredths of meters (or 22 decimal places)
Get tutor helpright-arrow

Posted 8 months ago

Question
Convert 1414 feet to meters using 3.2813.281 feet: 11 meter\newlineRound answers to hundredths of meters (or 22 decimal places)
Get tutor helpright-arrow

Posted 8 months ago

View all (114)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant