Problems C-1

a. Every ball has n choices. Hence .

b. By the hint, arrange n balls and b-1 sticks in a row. The begin to the first stick is in the first bin, and so on. So there are ways.

c. By the hint, arrange n identical balls and b-1 sticks in a row. So there are latex {b \choose n}$ ways.

e. We select b balls for every bin. So there are n-b balls that should be placed in b bins. There are ways.

Exercises C.5-7

Let be the right hand side of C.45. . Let , .

Exercises C.5-6

Solution Wanted!

Exercises C.5-5

Solution Wanted!

Exercises C.5-4

Solution Wanted!

Exercises C.5-3

Solution Wanted!

Exercises C.5-2

Solution Wanted!

Exercises C.5-1

Obtaining no heads when you flip a fair coin n times: .
Obtaining fewer than n heads when you flip the coin 4n times: by Chernoff’s bound.

Hence obtaining fewer than n heads when you flip the coin 4n times is less likely.

Exercises C.4-9

Solution Wanted!

Exercises C.4-8

Solution Wanted!