Answer:
Step-by-step explanation:
This is a Combination (as in permutation vs combination) question the symbol (n r) refers to "n choose r". This is sometimes written as nCr
i.e the question is asking you to find how many combinations each will yield when you chose r items from n item without repetition and order does not matter.
I will only do the first question for you and you can just follow the same steps to solve the rest of the questions.
Recall that

Consider question a) we are given (5 1) or ₅C₁
we can see that n = 5 and r = 1
If we substitute this into the formula:
₅C₁ = (5!) / [ (1!)(5- 1)!]
= (5!) / [ (5- 1)!]
= (5!) / (4!)
= (5·4·3·2·1) / (4·3·2·1)
= 5
hence ₅C₁ = 5
Answer: There are 456975758 plates that the state can issue.
Step-by-step explanation:
Since we have given that
Number of letters = 4
Number of numerals = 3
And 242 letter arrangements are not allowed.
As we have 26 letters i.e A-Z
and numerals i.e, 0-9
So, the number of plates would be

So, the restricted letters deducting would be

Hence, there are 456975758 plates that the state can issue.
Answer:
87
Step-by-step explanation:
earning rate (R) = $5/hr
total (T) = $287
time (t) = 40 hr
tips = T - Rt
= $287 - $5*40
$87
Standard Form of the circle:

For y:
y=3 (+/-)

For x:
x=