Hi there!
The key in the question is "divide". Therefore, we divide 5 by 3
5/3=1.6 pounds
I don't think any of these are right.
35 in. because a pentagon has 5 sides and have to divide the total amount of yarn to the sides.
Answer:
a. 205320
b. 34220
c. 60! / (35)! (25)! + 60!/ (40)!(20)! + 60!/ (45)! (15)!
Step-by-step explanation:
a) The number of ways to dustribute exams among the TA's is:
n / (n - r)!
n= number of things to choose from
r= Choosing r number
60P3= 60! / (60 - 3)!
(60)(59)(58)(57)! / (57)!
=205320
B) The number of ways to dustribute the exams among the TA's is:
n! /(n - r)! r!
60C3= 60! /(60 - 3)! 3!
= 60!/ 57! 3!
= 60 × 59 × 58 / 3 × 2 × 1
= 34220
C) The required number of ways is:
60C25 + 60C20 + 60C15
= 60! / (35)! (25)! + 60!/ (40)!(20)! + 60!/ (45)! (15)!
You can write 2311 and 3912 in the form 
:
Then
Taken modulo 20, the terms containing powers of 20 vanish and you're left with
We further have
so we end up with
and so 
.
###
If instead you're trying to find 
, you can apply Euler's theorem. We can show that 
using the Euclidean algorithm. Then since 
, and 8 divides 3912, we have
To show 2311 and 20 are coprime:
2311 = 115*20 + 11
20 = 1*11 + 9
11 = 1*9 + 2
9 = 4*2 + 1 => gcd(2311, 20) = 1
