MathDB

p13. Emma has the five letters:

A, B, C, D, E

. How many ways can she rearrange the letters into words? Note that the order of words matter, ie

ABC DE

and

DE ABC

are different.
p14. Seven students are doing a holiday gift exchange. Each student writes their name on a slip of paper and places it into a hat. Then, each student draws a name from the hat to determine who they will buy a gift for. What is the probability that no student draws himself/herself?
p15. We model a fidget spinner as shown below (include diagram) with a series of arcs on circles of radii

1

. What is the area swept out by the fidget spinner as it’s turned

60^o

? https://cdn.artofproblemsolving.com/attachments/9/8/db27ffce2af68d27eee5903c9f09a36c2a6edf.png
p16. Let

a,b,c

be the sides of a triangle such that

gcd(a, b) = 3528

gcd(b, c) = 1008

gcd(a, c) = 504

. Find the value of

a * b * c

. Write your answer as a prime factorization.
PS. You should use hide for answers. Collected [url=https://artofproblemsolving.com/community/c5h2760506p24143309]here.

Problem Statement