I draw numbers 1 through k (k≤10) out of a hat ten times at random, replacing the numbers after drawing them. If I disregard the case where I draw "1" all ten times, explain why the number of possible sequences is divisible by 11. (Result by a calculator is insufficient because anyone can do that easily.)

Now if I change the number '10' to another integer n in the above paragraph, can I still have a similar result; i.e., the total possible number of configurations is divisible by n+1? Does this work for all integers n? If so, prove it; if not, find all integers n it works for.

(In reply to re(5): Replace '10' by n by Richard)

Thanks! Finally see the problem. Though now I think the problem difficulty should be greater than 3.

Edited on September 5, 2006, 5:03 pm

Posted by Bractals on 2006-09-05 10:16:00