How many permutations of the 26 letters of the English alphabet do not contain any of the strings fish, rat, or bird
The number of permutations of the 26 letters of the English alphabet that do not contain any of the strings fish, rat, or bird is 402619359782336797900800000
Let
[tex]\mathcal{E}=\{\text{All lowercase letters of the English Alphabet}\}\\\\B=\overline{\{b,i,r,d\}} \cup \{bird\}\\\\F=\overline{\{f,i,s,h\}} \cup \{fish\}\\\\R=\overline{\{r,a,t\}} \cup \{rat\}\\\\FR=\overline{\{f,i,s,h,r,a,t\}} \cup \{fish,rat\}[/tex]
Then
[tex]Perm(\mathcal{E})=\{\text{All orderings of all the elements of } \mathcal{E}\}\\\\Perm(B)=\{\text{All orderings of all the elements of } \mathcal{E} \text{ containing bird}\}\\\\Perm(F)=\{\text{All orderings of all the elements of } \mathcal{E} \text{ containing fish}\}\\\\Perm(R)=\{\text{All orderings of all the elements of } \mathcal{E} \text{ containing rat}\}\\\\Perm(FR)=\{\text{All orderings of all the elements of } \mathcal{E} \text{ containing both fish and rat}\}\\[/tex]
Note that since
[tex]F \cap R=\varnothing[/tex], [tex]Perm(F)\cap Perm(R)\ne \varnothing[/tex]
But since
[tex]B \cap R \ne \varnothing[/tex], [tex]Perm(B)\cap Perm(R)= \varnothing[/tex]
and
[tex]B \cap F \ne \varnothing[/tex] , [tex]Perm(B)\cap Perm(F)= \varnothing[/tex]
Since
[tex]|\mathcal{E} |=26 \text{, then, } |Perm(\mathcal{E})|=26! \\\\|B|=26-4+1=23 \text{, then, } |Perm(B)|=23!\\\\|F|=26-4+1=23 \text{, then, } |Perm(F)|=23!\\\\|R|=26-3+1=24 \text{, then, } |Perm(R)|=24!\\\\|FR|=26-7+2=21 \text{, then, } |Perm(FR)|=21!\\[/tex]
where [tex]|Perm(X)|=\text{number of possible permutations of the elements of X taking all at once}[/tex]
and
[tex]|Perm(F) \cup Perm(R)| = |Perm(F)| + |Perm(R)| - |Perm(FR)|\\= 23!+24!- 21! \text{ possibilities}[/tex]
What we are looking for is the number of permutations of the 26 letters of the alphabet that do not contain the strings fish, rat or bird, or
[tex]|Perm(\mathcal{E})|-|Perm(B)|-|Perm(F)\cup Perm(R)|\\= 26!-23!-(23!+24!- 21!)\\= 402619359782336797900800000 \text{ possibilities}[/tex]
This link contains another solved problem on permutations:
https://brainly.com/question/7951365
You have 2\3 of a pizza left from yesterday. You divide it into 4 equal pieces. What fraction of the pizza is each piece?
Step-by-step explanation:
that means we divide 2/3 by 4.
2/3 / 4 = 2/3 / 4/1 = 2/3 × 1/4 = 2/12 = 1/6
so each quarter of the remaining 2/3 pizza is actually 1/6 of the complete pizza.
help algebra 2 100 pints if you answer right
Answer:
49x^4-70x^3+319x^2-420x+150, first option
Step-by-step explanation:
Just do (7x^3-5x^2+42x-30) times (7x-5)
and you will get 49x^4-35x^3-35x^3+25x^2+294x^2-210x-210x+150.
All this would simplify to the first option.
49x^4 - 35x^3 - 35x^3 + 25x^2 + 294x^2 - 210x - 210x + 150
= 49x^4 - 70x^3 + 319x^2 - 420x + 150
ANSwer: The first one.
In an attempt to predict a single response variable y, three models are estimated. The standard error of the estimate for Model 1 equals 10, for Model 2 equals 100, and for Model 3 equals 1000. According to the standard error of the estimate, which model provides the best fit
Where does the graph of y= sin x from x= 0 to x= 217 start?
O A.
at its minimum
O B.
at an x-intercept
O C.
at its maximum
OD.
between an x-intercept and its maximum
Answer:
at an x intercept
Step-by-step explanation:
You need to calculate sin 0 = 0. Which means it's crossing (or at least touching) the x axis.
can someone please help me solve this!
Answer:
B
Step-by-step explanation:
[tex]4x^{2}-11x-3=0\\4x^{2}-12x+x-3=0\\4x(x-3) + (x-3) = 0\\(4x+1)(x-3)=0[/tex]
B is factorable through this method
Solve the slope for the table.
the answer to your question is slope is 6
8
Which does NOT describe the quadrilateral below?
O A. trapezoid
B. square
C. parallelogram
О
D. rectangle
Can I get some help on this I have so many assignments to do and I just want to go to sleep
PLEASE HELP!!!
what is the value of the expression 2/5m−1/3 when m = 3?
Answer:
13/15
Step-by-step explanation:
I took the quiz and solved it out. I would give further explaination but it is kinda hard to do that in text form. Have a nice day!
The value of the expression if m = 3 is 13/15
Given the expression as shown below:
2/5 m - 1/3If the value of m = 3, hence the expression will become;
2/5(3) - 1/3
6/5 - 1/3
Find the LCM
6/5 - 1/3 = 3(6)-5/15\
6/5 - 1/3 = 18-5/15
6/5 - 1/3 = 13/15
Hence the value of the expression if m = 3 is 13/15
Learn more on equations here: https://brainly.com/question/13763238
Which of the following is a run on sentence
Answer:
B.
Step-by-step explanation:
There is no pause and the use of a connection word (and) makes the sentence seem longer. Hope this helps :) brainliest?? <3
I GIVE BRANLIEST. Question is on the bottom
Answer:
432
24*36
---------- = 432
2
MP Construct Arguments Raul finds a way to divide
48 building blocks into 6 equal groups. Jerry finds a
way to divide 48 building blocks into 8 equal groups.
Whose way has the greater number of building blocks
in each group? Explain.
Answer:
Raul
Step-by-step explanation:
Since 8 groups of building blocks has a smaller amount than 6 equal groups of building blocks, so Raul has more blocks in each group
942 flowers in157 vases= flowers per vase
Answer : 942/157 = 6
I'm taking the ssat upper level on December 11th and really need help with the math section. Are there any tips or help that can be provided?
Answer:
1, Stay calm
2, be confident
3, if you know the type of questions they are gonna ask practiece those type of questions
Also good luck
Which function has the greater maximum value: f(x) = -3x + 6x+4, or g(x),
the function in the graph?
у
5
g(x)
х
O A. The functions have the same maximum value.
B. g(x)
O C. f(x)
CAN SOMEONE HELP ME PLEASE ASAP!
Answer: ≈ 26 lb
Step-by-step explanation:
11,800 grams x [tex]\frac{1 kilograms}{1000 grams}[/tex] x [tex]\frac{1 pound}{0.45kilograms}[/tex] ≈ 26 lb
mabel spent 4 hours editing a 3 minute long video she edits at a constant ratehow long does mabel spent to edit a 9 minute video
4/3=1.3 repeating
1.3repeatingx9= 12/9
Please help I don’t understand this
Answer:
The area is 24
Step-by-step explanation:
Divide the quadrilateral into 4 triangles (two identical at the top and two identical at the bottom).
Then find the area of each triangle and add it all together
Area of Triangle= (base x height)/2
(3 x 3)/2 + (3 x 3)/2 + (5 x 3)/2 + (5 x 3)/2
this equation gives us 24 as the area
help me please!!!!!!!!!!!
Answer:
I did mostly everything for you bestiieee on the pictureee :3
Step-by-step explanation:
hope this helped :3
:3 byeeeeeeeeeee
You have 20 quarters. You find 40% more in your room. Then you go to the store and spend 50% of them. How much money do you have left? please answer the question without a link
Answer:
14
Step-by-step explanation:
First fond 40% of 20
20×40/100 = 8
So now there is a total of 20+8 =28
At the store you spend exactly half
28×50/100 =14
So now you are left with 28-14 =14
3/10 = ___ x 1/10
pls help i'll give brainiest
Answer:
1/10 x 30/10=30/100 then simplify =3/10
Step-by-step explanation:
Hope I helped please mark brainliest!
Mackenzi is buying school supplies. She needs to buy 30 writing utensils so that she doesn't run out during the year
but only has $20.90 saved up. If pencils are $0.35 and pens are $0.95 at the school store, how many of each could
she get if she spent all of her savings?
х
Answer the following questions. Round your answers to the nearest whole numbers.
How many pencils can she buy?
How many can she buy?
*Help ASAP please!*
She can buy 16 pens and 16 pencils.
pls help asap MIDSEGMENTS
Answer:
Angle 2 = 64°
Step-by-step explanation:
Angle 2 = 180°-116° (int angles, 12//34)
=64°
x^3 - 3x^2 + 4x - 12
Answer:
(x^2 + 4)(x - 3).
Step-by-step explanation:
I'm guessing you want to factor this.
You can do it by grouping:
x^3 - 3x^2 + 4x - 12
= x^2(x - 3) + 4(x - 3)
= (x^2 + 4)(x - 3).
Choose ALL of the transformations that have been applied to the linear function below.
()=−2−4
(It’s multiple choice)
1.Reflected over x-axis
2.Vertical stretched
3.Shifted down 4
4.None of the above
Does anyone know this ??
bbbbbbbbbbbbbbbbbbbbbbbbbbbvbbbbbbbbbbb
There is a bag filled with 3 blue, 4 red and 5 green marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting exactly 1 green?
Answer:
35/72
Step-by-step explanation:
Michaela and Aleah play on the same basketball team. In one game Michaela scored one fifth of the team's points and aleah scored one tenth's of the team's points. Together the scored a total of 42 points. How many points did the team score?
Colin invests £980 into his bank account. He receiv 0.3% per year simple interest. How
much will Colin have after 7 years? Give your answer to the nearest penny where appropriate.
Answer: 1,000.77
Step-by-step explanation:
After 1 year: 980 + 0.3% = 982.94
After 2 years: 982.94 + 0.3% = 985.89
After 3 years: 985.89 + 0.3% = 988.85
After 4 years: 988.85 + 0.3% = 991.82
After 5 years: 991.82 + 0.3% = 994.80
After 6 years: 994.80 + 0.3% = 997.78
After 7 years: 997.78 + 0.3% = 1,000.77
Brainliest?