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
Donuts because I really like them
Answer:
Step-by-step explanation:
cos(x) = sin(15°)
x = arccos(sin(15°)) = 75°
Answer:
y=(1/3)x- 4/3
Step-by-step explanation:
If two lines are perpendicular to each other, then the slopes will be the negative inverse to each other.
Example:
the negative inverse of 2 is -1/2
the slope of
is -3
the negative inverse of -3 is 
So we have the perpendicular line be :
Since it also go through (4,0)
plug in we get 

So the equation would be

4x + 6 = -10<span>Simplifying
4x + 6 = -10
Reorder the terms:
6 + 4x = -10
Solving
6 + 4x = -10
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-6' to each side of the equation.
6 + -6 + 4x = -10 + -6
Combine like terms: 6 + -6 = 0
0 + 4x = -10 + -6
4x = -10 + -6
Combine like terms: -10 + -6 = -16
4x = -16
Divide each side by '4'.
x = -4
Simplifying
x = -4</span>