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?
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