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wu :: forums    riddles    hard (Moderators: Grimbal, SMQ, william wu, ThudnBlunder, Eigenray, Icarus, towr)    Color Balls in a bag « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Color Balls in a bag  (Read 685 times) ERIC H. ZENGULUS Newbie     Posts: 11 Color Balls in a bag   « on: Jun 27th, 2004, 10:28am » Quote Modify There are N balls in the bag. Each one has a distinct color. You draw one ball randomly from the bag, record its color and put it back. Calculate the probability that after T draws you've seen M distinct colors.   (T > 0, M > 0, M <= min(T, N) ) « Last Edit: Jul 19th, 2004, 7:52pm by Icarus » IP Logged Nigel_Parsons Junior Member     Gender: Posts: 63 Re: NEW: HARD: Color Balls in a bag   « Reply #1 on: Jun 27th, 2004, 5:28pm » Quote Modify A bit difficult this one!   It relies on the assumption (not stated) that N>M, also that T  [smiley=eqslantgtr.gif] M   Otherwise, it may be worth considering!   If either of the above is not the case then the possibility is Zero IP Logged ThudnBlunder wu::riddles Moderator Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Re: NEW: HARD: Color Balls in a bag   « Reply #2 on: Jun 27th, 2004, 7:11pm » Quote Modify on Jun 27th, 2004, 5:28pm, Nigel_Parsons wrote: A bit difficult this one!   It relies on the assumption (not stated) that N>M, also that T  [smiley=eqslantgtr.gif] M   If either of the above is not the case then the possibility is Zero No. For example, when N = M = T required probability = N!/NN   So now you should be able to finish it off.     « Last Edit: Jun 27th, 2004, 8:25pm by ThudnBlunder » IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. Barukh Uberpuzzler     Gender: Posts: 2276 Re: NEW: HARD: Color Balls in a bag   « Reply #3 on: Jun 28th, 2004, 12:08am » Quote Modify [smiley=blacksquare.gif] I get for the general case the following: NCM [sum]1 [le] k [le] M(-1)M-k MCk (k/N)T.   Compare it to THUD&BLUNDER’s answer for M=T=N case.   [smiley=blacksquare.gif] IP Logged Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------  - easy   - medium => hard   - what am i   - what happened   - microsoft   - cs   - putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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