1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Luden [163]
3 years ago
11

How many ways can eight letters be arranged into groups of five where order matters and the first two letters are already chosen

?
Mathematics
2 answers:
fenix001 [56]3 years ago
6 0

Answer:

120

Step-by-step explanation:

Since we're dealing with a problem where the order matters and the first two letters are already chosen we need to subtract the number of letters and the number of available slots per group.

We use the permutation formula to find the answer, but before that let's check values.

n = 8

k = 5

Now since there are two letters already chosen we have to deduct two from both the value of n and k.

n = 6

k = 3

Now we can use the permutation formula:

_{n}P_{k}=\dfrac{n!}{(n-k)!}

_{6}P_{3}=\dfrac{6!}{6-3)!}

_{6}P_{3}=\dfrac{6!}{3!}

_{6}P_{3}=\dfrac{6*5*4*3*2*1}{3*2*1}

The 3*2*1 cancels out and leaves us with:

_{6}P_{3}=6*5*4

_{6}P_{3}=120

So there are 120 possible ways to arrange eight letters into groups of five where order matters and the first two letters are already chosen.

Paraphin [41]3 years ago
6 0

This problem is based on permutations because here order matters.

This problem can be found by the following solution.

When you are given 8 letters and two letters are already chosen, then 6 letters are left and you want to know in how many ways 6 letters can fill 3 spaces when order matters. So, the answer is 6P3 ways.

\frac{6!}{(6-3)!}

= \frac{6 *5 *4 *3 *2 *1}{3 *2 *1}

= 6*5*4 = 120

Hence, there are total 120 combinations.

You might be interested in
Find the median of this data: 18, 9, 17, 18, 15, 10, 18. If necessary, round to the nearest tenth.
Marta_Voda [28]
9, 10, 15, 17, 18, 18, 18

17

3 0
3 years ago
Find the product. (n 7)2 n² 14n 14 2n² 14n 49 n² 14n 49.
Marianna [84]

The product of \rm (n+7)^2 is \rm n^2+14n+49.

Given

The product of \rm (n+7)^2.

<h3>What is multiplication?</h3>

Multiplication is the process of calculating the product of two or more numbers.

The multiplication of numbers say, ‘a’ and ‘b’, is stated as ‘a’ multiplied by ‘b’.

The product of \rm (n+7)^2 is given by;

\rm =(n+7)^2\\\\=(n+7)\times (n+7)\\\\= n(n+7)+7(n+7)\\\\=n^2+7n+7n+49\\\\=n^2+14n+49

Hence, the product of \rm (n+7)^2 is \rm n^2+14n+49.

To know more about Multiplication click the link given below.

brainly.com/question/19943359

8 0
2 years ago
Which rules could describe the rotation? Select two options
nasty-shy [4]
Find the price and quantity
Qs=p2 + 2ps-15
3 0
3 years ago
Complete the table for the following function<br> y=(1/3)^x
Bumek [7]

x=-3 then y= 27

x= -2 then y= 9

x=2 then y: y=\frac{1}{9}

x=3 then y: y=\frac{1}{27}

The graph of the function decreases from left to right.

Option C is correct.

Step-by-step explanation:

We are given the function: y=(\frac{1}{3})^x

and we need to fill the table

if x = -3 then y=?

Putting value of x in the given function:

y=(\frac{1}{3})^x

y=(\frac{1}{3})^-3

Applying exponent rule a^-b= 1/a^b

y=\frac{1}{(\frac{1}{3})^3 }\\y=\frac{1}{\frac{1}{27}}\\y=27

if x = -2 then y=?

Putting value of x in the given function:

y=(\frac{1}{3})^x

y=(\frac{1}{3})^-2

Applying exponent rule a^-b= 1/a^b

y=\frac{1}{(\frac{1}{3})^2 }\\y=\frac{1}{\frac{1}{9}}\\y=9

if x = 2 then y=?

Putting value of x in the given function:

y=(\frac{1}{3})^x

y=(\frac{1}{3})^2

Applying exponent rule a^-b= 1/a^b

y=\frac{1}{(\frac{1}{3})^2 }\\y=\frac{1}{9}

if x = 3 then y=?

Putting value of x in the given function:

y=(\frac{1}{3})^x

y=(\frac{1}{3})^3

Applying exponent rule a^-b= 1/a^b

y=\frac{1}{(\frac{1}{3})^3 }\\y=\frac{1}{27}

So, x=-3 then y= 27

x= -2 then y= 9

x=2 then y: y=\frac{1}{9}

x=3 then y: y=\frac{1}{27}

Graph of the function is shown in figure attached.

The graph of the function decreases from left to right.

Option C is correct.

Keywords: Solving Equations

Learn more about Solving Equations at:

  • brainly.com/question/1563227
  • brainly.com/question/2403985
  • brainly.com/question/11229113

#learnwithBrainly

7 0
3 years ago
Leona has a bag containing letter tiles. Which describes dependent events?
serious [3.7K]

Answer:

a) removing a vowel, not replacing it, and then removing another vowel

Step-by-step explanation:

This question is from the topic Probability. In Probability, a dependent event is one in which the outcome of one event alters or changes the outcome of another event. <u>A classic example of this is seen when sampling without replacement is done</u>. When sampling without replacement is done, the outcome of another event within the same set changes. When sampling with replacement is done, the outcome of the events are independent because every item in the population still has an equal chance of being chosen. However, in the case of sampling without replacement, once an item has been selected from a population, the outcome of every other event after it is altered based on the item that was initially chosen.

Let's assume that the bag has 26 tiles (one for each alphabet from a - z)

Population = 26, consonant = 21, vowel = 5

If a vowel or consonant is removed & is replaced, we have:

Pr (choosing "a") = number of item ÷ population

Pr = 1 ÷ 26 = 1/26

Pr (choosing "y") = 1 ÷ 26 = 1/26

Doing this for over & over again, produces the same probability

However, if an item was selected without replacement, we have:

Pr (choosing "a") = 1 ÷ 26 = 1/26

Without replacement implies that if I choose tile letter "a", tile letter "a" will not be included in subsequent events, hence:

Population = 25

Pr (choosing "u") = 1 ÷ 25 = 1/25

Without replacement, population = 24

Pr (choosing "y") = 1 ÷ 24 = 1/24

So, we see the dependent nature of the events in how that the outcome of the next event is being altered. <u>As such, </u><u>option a</u><u> describes a dependent event & is the correct answer</u>

8 0
3 years ago
Other questions:
  • Perimeter is 46 ft length is 10 ft what is width
    5·1 answer
  • Expand and simpilify (x+2)(x+1)
    8·1 answer
  • Math help I need help with all 4 questions
    14·1 answer
  • Martha has 20 more Oreos than Theo. Cla
    8·1 answer
  • The radius of a circle is 5 m. Find its area to the nearest tenth.
    5·1 answer
  • What will the horizontal cross of a cone be​
    7·1 answer
  • What is m&lt;1 equal to
    11·1 answer
  • I really REALLY need the work for these 5 math problems, I can't wrap my brain around how to understand how to do this still and
    7·1 answer
  • The measures of two complementary angles are represented by (2x) and (3x - 10)". What is the value of x?
    9·1 answer
  • 1) In the figure below, m_2 = 60°. Find the measure of each angle. Write which postulate(s) or
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!