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

Then

Note that since
, 
But since
, 
and
, 
Since

where 
and

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

This link contains another solved problem on permutations:
brainly.com/question/7951365
Answer:

Step-by-step explanation:
In this exercise, we have two equations, namely:

And we are asked to solve this problem by graphing. In this way, we can write a system of linear equations in two variables, but first of all, let's rewrite:

Then:

So here we have two lines.
The first one is:

This line passes through the origin and has a slope 
The second one is:

This line has a slope
and cuts the y-axis at 
By using graph tools, we get the graph shown below, then:

Answer:
It is (x+ 1
Step-by-step explanation:
Because -1 is a root because 4(-1)^3 + 9(-1)^2 - (-1) - 6 = -4 + 9 + 1 - 6 = -5 + 5 = 0
Answer:
100
Step-by-step explanation:
Given that 2 ap's have same common difference
given that their 100th terms difference is 100
let the first no. of first series be a1 and second series be a2
then, a(1)100 - a(2)100=100 ---- 1
for 1st series ---- a100=a1+99d
2nd series ---- a100 = a2+99d
keep these values in (1)
then,
a1+99d - (a2+99d) = 100
a1+99d-a2-99d=100
therefore, a1-a2 =100 ------------------------------------------- 2
then the difference between their 1000th terms is
for 1st series --- a1000 = a1+999d
for 2nd series --- a1000 = a2+999d
their 100th terms difference is
a(1)1000-a(2)1000
a1+999d-(a2+999d)
a1+999d-a2-999d
therefore we get the value a1-a2
from (2) a1-a2 = 100
therefore the difference between their 1000th terms is 100
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That's what I got. to rationalize the numerator you have to multiply by the conjugate, in this case (√3 + 9) / (√3 + 9), which is what it looks like you did.
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