Answer:
We want to find:
Here we can use Stirling's approximation, which says that for large values of n, we get:
Because here we are taking the limit when n tends to infinity, we can use this approximation.
Then we get.
Now we can just simplify this, so we get:
And we can rewrite it as:
The important part here is the exponent, as n tends to infinite, the exponent tends to zero.
Thus:
Answer:
Step-by-step explanation:
To aid in understanding, draw three circles...
100 were registered for both Math and English.
50 were registered for both Sport and English but not Math.
70 were registered for Math, Sport, and English.
From here we will be able to calculate for those that signed up for only English class: Total number of students that signed up for english class
a. none signed up only for Maths (refer to attached document)
b. How many signed up for neither Math nor English meaning they signed up for only sports which is 70 from the venn diagram in the attachment.
c. How many signed up for an English class and at least one other class?
From the venn diagram:
we could have an English class and maths class - 100
we could also have an a English class and sports - 50
Thus total is 150.
d. What is the total fee for all the students enrolled in classes
From the diagram, 120 (english only and sport only) enrolled for only one class = 120 x $100 = $12,000
From the diagram, 180 (english and sport, maths and sport and english and maths) enrolled for two classes = 180 x $150 = $27,000
From the diagram, only 70 enrolled for the three classes = 70 x $200 = $14,000
Total fees = $12,000 + $27,000 + $14,000 = $53,000
