Problem C « Exercise Lover

March 28, 2007

Problems C-1

Filed under: Problem C — yuhanlyu @ 3:48 pm

a. Every ball has n choices. Hence $b^n$ .

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 $(b+n-1)!/(b-1)!$ ways.

c. By the hint, arrange n identical balls and b-1 sticks in a row. So there are ${n+b-1 \choose n} ways.</p> <p>d. Among the b bins, we choose n bins to place the ball. So there are$ 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 ${n-1 \choose b-1}$ ways.