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 10-letter arrangements that can be formed using the letters in the word STATISTICS?
Answer:

What is the total number of different $10$ -letter arrangements that can be formed using the letters in the word STATISTICS? $\newline$ Answer:

View step-by-step help

View step-by-step help

Find the magnitude of a three-dimensional vector

Full solution

Q. What is the total number of different

10

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

\newline

Answer:

Word Frequency: The word STATISTICS has $10$ letters in total, with the following frequency of each letter: $S$ occurs $3$ times, $T$ occurs $3$ times, $A$ occurs $1$ time, $I$ occurs $2$ times, and $C$ occurs $1$ time.
Permutations Formula: To find the total number of different 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 frequencies of each distinct item.
Calculation of Frequencies: In this case, $n = 10$ (total letters), $n_1 = 3$ (for S), $n_2 = 3$ (for T), $n_3 = 1$ (for A), $n_4 = 2$ (for I), and $n_5 = 1$ (for C).
Factorial Calculation: Now we calculate the factorial of each of these numbers: $10! = 3,628,800$ , $3! = 6$ , $2! = 2$ , and $1! = 1$ .
Application of Formula: We then apply the formula: $10! / (3! * 3! * 1! * 2! * 1!) = 3,628,800 / (6 * 6 * 1 * 2 * 1) = 3,628,800 / 72 = 50,400$ .
Total Arrangements: Therefore, the total number of different $10$ -letter arrangements that can be formed using the letters in the word STATISTICS is $50,400$ .

More problems from Find the magnitude of a three-dimensional vector

Question

Rewrite in simplest terms:

6 c-9(-2 c-9)

\newline

Posted 8 months ago

Question

Find the coordinates of the vertex of the following parabola using graphing technology. Write your answer as an

(x, y)

\newline

y=-2 x^{2}-12 x-2

\newline

Posted 9 months ago

Question

Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an

(x, y)

\newline

y=-2 x^{2}-18

\newline

Posted 9 months ago

Question

Write the equation of the line that passes through the points

(-1,-4)

(6,-8)

. Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

\newline

\newline

Posted 9 months ago

Question

Find the distance between

P(4,4)

Q(9,7)

\newline

The distance between

P

Q

\square

\newline

(Simplify your answer. Type an exact answer using radicals as need

Posted 8 months ago

Question

\begin{aligned} x+y&=3, \ & x-3y=-9 \end{aligned}

\newline

What is the solution

(x,y)

to the given system of equations?

Posted 8 months ago

Question

6

. The length and breadth of a room are

3 x^{2} y^{3}

6 x^{3} y^{2}

. Find its and area.

Posted 8 months ago

Question

Without dividing, determine if

77

269

is divisible by

2

and explain how you know.

\newline

77,269 \square

2

Posted 8 months ago

Question

Without dividing, determine if

46

264

is divisible by

9

and explain how you know.

\newline

46,264 \square

9

Posted 8 months ago

Question

Which number represents the probability of an event that is certain to occur?

\newline

\frac{39}{20}

\newline

1

\newline

\frac{1}{100}

\newline

\frac{83}{100}

Posted 8 months ago

Related topics

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