Answer :
The probability that no two neighboring beads are the same color is 1/12.
Define probability.
According to the probability formula, the likelihood that an event will occur is equal to the proportion of favorable outcomes to all outcomes. Number of favorable outcomes/Total Number of outcomes determines the probability that an event will occur, P(E).
Given,
The beads on the line are arranged in distinct sequences. We have the following setups that satisfy the necessary condition:
6!/3!2!1! = 120
Case 1:
We have 3!/2! × 2 = 6
Configurations exist.
We have,
2 × 2 = 4
There are therefore 10/120 orders that satisfy the necessary criterion.
The probability is 10/120 = 1/12
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