## Trending News

# 緊急, 數學高手請幫幫手

1. In the mysterious lost city of Mim, the length of daylight (in hours) on the

圖片參考：http://r140.n100.queensu.ca:8081/wwtmp/equations/e...

Use this model to compare how the number of hours of daylight is increasing on March 16 and June 2 (assume that this is a standard year, not a leap year).

2. A Norman window has the shape of a semicircle atop a rectangle so that the diameterof the semicircle is equal to the width of the rectangle. What is the area of the largestpossible Norman window with a perimeter of 48 feet?

### 1 Answer

- KevinLv 78 years agoFavorite Answer
It is better to use the negation and the fact P(AUB) = P(A) + P(B) - P(A∩B) in this question

No restriction:

Number of all possible arrangements = 7P7 = 5040

V is at its original position:

Number of possible arrangements = 6P6 = 720

T is at its original position:

Number of possible arrangements = 6P6 = 720

V and T are both at their original position:

Number of possible arrangements = 5P5 = 120

Applying P(AUB) = P(A) + P(B) - P(A∩B),

Either V or T is at its original position:

Number of possible arrangements = 720+720-120 = 1320

Using the negation,

Number of possible arrangements = 5040-1320 = 3720Another method:

T is at the first place:

V can be at any other place, number of possible arrangements = 6P6 = 720

T is at the 2,3,5,6,7th place(5P1):

V can be at any other place except the first, number of possible arrangements = 5P1*5P1*5P5 = 3000

adding all cases and get 720+3000 = 3720

- Login to reply the answers