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Three black beads, two red beads, and a yellow bead are arranged in a line. What is the probability that no black bead is adjacent to the yellow bead?

 Mar 7, 2020
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We  have    6!  /[3! * 2!]   =  60   distinguishable configurations

 

I  get that  there 12  configurations  where  no black bead is  next to the yellow one  : 

 

YRRBBB    RYRBBB   BBBRRY

YRBRBB    BRYRBB   BBRBRY

YRBBRB    BBRYRB   BRBBRY

YRBBBR    BBBRYR   RBBBRY

 

 

So ....the  probability is  12  / 60   =   1  / 5

 

 

 

cool cool cool

 Mar 7, 2020
edited by CPhill  Mar 7, 2020

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