Question

Assume that there are five groups of triplets. They are assigned randomly to a row of 15 seats.What is the probability that none of the triplets sit next to each other.

Answer 1

Solution:- The probability that none of the triplets sit next to each other = 0.97143.

n = 15,

Let first find the probability when all the twins sit together.

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Number of arrangements of three twins in seating of 15= 13!

Twins can also be arranged in themselves = 3!

Total number of arrangements of three twins in seating = 13!*3! = 37,362,124,800

Total number of arrangements of 15 members = 15!

The probability that all the triplets sit next to each other = (37,362,124,800)/15! = 0.02857

The probability that none of the triplets sit next to each other = 1 - 0.02857 = 0.97143