MathDB

p1.

4

balls are distributed uniformly at random among

6

bins. What is the expected number of empty bins?
p2. Compute

{150 \choose 20 }

(mod

221

).
p3. On the right triangle

ABC

, with right angle at

B

, the altitude

BD

is drawn.

E

is drawn on

BC

such that AE bisects angle

BAC

and F is drawn on

AC

such that

BF

bisects angle

CBD

. Let the intersection of

AE

and

BF

G

. Given that

AB = 15

BC = 20

AC = 25

, find

\frac{BG}{GF}

.
p4. What is the largest integer

n

so that

\frac{n^2-2012}{n+7}

is also an integer?
p5. What is the side length of the largest equilateral triangle that can be inscribed in a regular pentagon with side length

1

?
p6. Inside a LilacBall, you can find one of

7

different notes, each equally likely. Delcatty must collect all

7

notes in order to restore harmony and save Kanto from eternal darkness. What is the expected number of LilacBalls she must open in order to do so?
PS. You had better use hide for answers.

round 2

Problems(1)