Problem Contest - Problem of the Week - April 20, 2004

Rolling the dice: Roll n fair k-sided dies (as in dice) all at once. What is the probability that you get exactly d different outcomes showing, with 0<d<=min(k,n)? Find a recursive solution. (This problem generalizes one that was solved successfully in early March. May have interest for computer science students too!)

For k=6. Total number of outcomes = 6^n

Some good outcomes for n=5 and d=3 Good outcomes for n=7 and d=4:
11156 1236666
11556 1211366
51156
15615

Submit written solution with justification to John Emerson, Warner 312, before 3:00 on Tuesday, April 27. Or leave them in the Warner mailroom.

Note: Join us at the weekly seminars, usually on Tuesday at 3:00 for refreshments.