Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

What is the total number of different 11-letter arrangements that can be formed using the letters in the word GALVANIZING?
Answer:

What is the total number of different $11$ -letter arrangements that can be formed using the letters in the word GALVANIZING? $\newline$ Answer:

View step-by-step help

View step-by-step help

Convert between customary and metric systems

Full solution

Q. What is the total number of different

11

-letter arrangements that can be formed using the letters in the word GALVANIZING?

\newline

Answer:

Word Analysis: The word GALVANIZING has $11$ letters with the following counts of identical letters: $G-2$ , $A-2$ , $N-2$ , $L-1$ , $V-1$ , $I-1$ , $Z-1$ .
Permutations Formula: To find the total arrangements, we use the formula for permutations of a multiset: $\frac{n!}{n_1! \times n_2! \times \ldots \times n_k!}$ , where $n$ is the total number of items to arrange, and $n_1, n_2, \ldots, n_k$ are the counts of identical items.
Calculate $11!$ : So, we calculate $\frac{11!}{(2! \cdot 2! \cdot 2!)}$ to account for the repeated G's, A's, and N's.
Calculate $2!$ : Calculating $11!$ gives us $39916800$ .
Calculate Total Sets: Calculating $2!$ for one set of identical letters gives us $2$ .
Divide to Get Total: Since we have three sets of identical letters, we calculate $2! \times 2! \times 2!$ which equals $8$ .
Divide to Get Total: Since we have three sets of identical letters, we calculate $2! \times 2! \times 2!$ which equals $8$ .Now, we divide $39916800$ by $8$ to get the total number of different arrangements.
Divide to Get Total: Since we have three sets of identical letters, we calculate $2! \times 2! \times 2!$ which equals $8$ .Now, we divide $39916800$ by $8$ to get the total number of different arrangements. $39916800 \div 8$ equals $4989600$ .

More problems from Convert between customary and metric systems

Question

\newline

1

2

\_\_\_\_\_

Posted 7 months ago

Question

710

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.)

Posted 8 months ago

Question

A real estate purveyor purchases a

60

000

\left(\mathrm{ft}^{2}\right)

warehouse and decides to turn it into a storage facility. The warehouse's width is exactly

\frac{2}{3}

of its length. What is the warehouse's width? Round your answer to the nearest foot.

Posted 8 months ago

Question

3

cups (c) of flour to bake

2

loaves of bread. If

1

pound (lb) of flour is equivalent to

3 \frac{1}{3} \mathrm{c}

, how many loaves of bread can the baker make with a

10 \mathrm{lb}

\newline

(Round the answer to the nearest whole number.)

Posted 7 months ago

Question

\$ 2500

into a savings account.

\newline

The relationship between the time,

t

, in years, since the account was first opened, and Ella's account balance,

B(t)

, in dollars, is modeled by the following function.

\newline

B(t)=2500 \cdot e^{0.025 t}

\newline

What will the balance of Ella's savings account be after

4

years? Round your answer, if necessary, to the nearest hundredth.

\newline

\$

Posted 8 months ago

Question

Maya needs to rent a car while on vacation. The rental company charges

\$17.95

18

cents for each mile driven. If Maya only has

\$40

to spend on the car rental, what is the maximum number of miles she can drive?

\newline

\newline

(Round your answer down to the nearest whole mile)

Posted 8 months ago

Question

What is the area of a circle whose circumference is

1447

\pi=3.14

166698.73\,\text{m}^2

Posted 8 months ago

Question

What is the area of a circle whose circumference is

1447

\pi = 3.14

166698.73 \, \text{m}^2

Posted 7 months ago

Question

13

feet to meters using

3.281

1

\newline

Round answers to hundredths of meters (or

2

decimal places)

Posted 8 months ago

Question

14

feet to meters using

3.281

1

\newline

Round answers to hundredths of meters (or

2

decimal places)

Posted 8 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant