perplexus.info :: Probability : Colored Bead Combos

Colored Bead Combos (Posted on 2006-12-17)

Consider an urn with 12 beads, four of each color: red, yellow and blue. Pull these beads out in pairs. What is the probability that among these six pairs, every color combination is represented?

Consider an urn with 30 beads, 10 of each color. Pull these beads out in triplets. What is the probability that every color combination is represented?

Submitted by Jer

Rating: 3.0000 (3 votes)

Solution: (Hide)

4!*4!*4!*2³*6!/12!
=64/385
=.166233766
Each 4! represents fact that it doesn't matter which red (or other) bead is pulled in each pair. The 2³ is because the ordering of each pair is unimportant. The 6! is because the order in which the pairs was pulled is unimportant.
10!*10!*10!*3⁶*6*10!/30!
=12597120/4105553009
=.002859373

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Answer	K Sengupta	2008-10-09 05:05:07
Part I (the long solution)	Steve Herman	2006-12-17 17:21:08
solution	Charlie	2006-12-17 13:00:07

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