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
one third of the result of three times a number that is increased by 12
Answer:
Step-by-step explanation:
1/3 (3x+12)
1/3×3x+1/3×12
x+4
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?
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
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!
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
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
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
Can I get some help on this I have so many assignments to do and I just want to go to sleep
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
1 + 1 PLEASE HELP AN EXPERT CANT EVEN ANSWER THIS
Answer:
1+1=2!!!!!!!!
YAY HAHAHAHAHAHA
Simplify the following.
can someone pls help 25+ Points And BRAINLIEST.
I know the answer so give step by step explanation.
Answer:
(2f-17h)/24k
Step-by-step explanation:
We can make the common denominator for 3k and 8k in the form of 24k, so we get (multiply the first fraction by 8 and the second one by 3 to get 24k on each denominator) (8f-32h)/3k-(6f-15h)/24k. Now we can just subtract the numerators :
8f-32h-6f+15h (sign gets flipped on 6f and 15h), so we get
(2f-17h)/24k
Solve the slope for the table.
the answer to your question is slope is 6
Carlisle purchased one-fourth of a pound of candy at the mall. What decimal did he see on the scale?
0.25
0.40
0.20
0.14
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
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
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.
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:
What is the greatest common factor of 18, 6, and 36?
Answer:
18 is the greatest common factor between those
Answer:
There are 6 common factors of 18 and 36, that are 1, 2, 3, 6, 9, and 18. Therefore, the greatest common factor of 18 and 36 is 18.
Step-by-step explanation:
place the comma in the position in the answer
[tex]4.7 \times 2.9 = 1316[/tex]
First of all, 4.7 * 2.9 = 13.63, so I think a mistake has occurred there and second, comma does not come here because this is not a big number, it is a small number. If you meant a dot instead. it would placed in the middle AKA 13.63
Would appreciate brainliest <3
Does anyone know this answer??
Answer:
In My Opinion, y < 425 - x
I hope this helps.
pls help asap MIDSEGMENTS
Answer:
Angle 2 = 64°
Step-by-step explanation:
Angle 2 = 180°-116° (int angles, 12//34)
=64°
a= 1 2 3 4 5 is the solution of a set of the variable equation
3x=15
Answer:
3x = 15
x = 15/3
x =5
8
Which does NOT describe the quadrilateral below?
O A. trapezoid
B. square
C. parallelogram
О
D. rectangle
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.
16.093 x 10 to the third power
HELP ME PLEASE GOD
Answer:
16093
Step-by-step explanation:
I hope this helps!
Answer:
Your answer is 6,960,212.797357.
End of Answer
Step-by-step explanation:
(19.093 * 10)^3 OR
19.093 * 10 = 190.93
190.93^3 = 6,960,212.797357
End of Step-by-step explanation
Edit: I'm probably wrong this is the actual answer: 16093
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
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).
942 flowers in157 vases= flowers per vase
Answer : 942/157 = 6
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.
